## Spring 2016 Schedule

April 25th

TeX Exchange Workshop

Led by: Massy Khoshbinp

Michael, Cindy, and Jon will be presenting on TikZ, Beamers, and Git/GitHub/Bitbucket. We recommend coming in with TeX running on your machine and Git installed (or your online Git repository opened). The follow are download links for installing Git:

Windows: https://git-for-windows.github.io
Linux: $sudo apt-get install git Here are links for downloading the TikZ and Beamer packages: https://www.ctan.org/pkg/pgf (tikz) https://www.ctan.org/pkg/tikz-cd (tikz-cd, which is good for drawing commutative diagrams) https://www.ctan.org.pkg/beamer (beamer) May 9th Title: Fuzzy Logic + Functional Equations + Knots and Lassos in Proteins = Fresh Mathematical Mixture from Poland Speaker: Wanda Niemyska, UCSB In the talk I would like to present the solutions to one nice functional equation: h(xg(y)) = h(x) + h(xy), x, y ∈ (0, ∞), and its connection to Fuzzy Logic and efficient working of our washing machines. I will start with a brief introduction to fuzzy operators and fuzzy control systems. I will explain how some specific properties (namely: distributivity) of fuzzy operators may speed up making decisions in fuzzy control systems. While studying distributivity of fuzzy implications in my PhD dissertation I had to solve a few functional equations. On Monday I want to present the one that I like maybe the most. (And finally I would like to give a few thoughts about my experience being a woman-mathematician in Poland). ## Date ## Winter 2016 Schedule January 4th Organizational Meeting January 25th Mentor and Mentee Meetup Come hang out with your mentors again, now that you've been here for a while. March 7th Title: A Discussion on the Tangle Model: An Application of Topology Speaker: Candice Price, Sam Houston State The tangle model was developed in the 1980's by professors DeWitt Sumner and Claus Ernst. This model uses the mathematics of tangles to model protein-DNA binding. An n-string tangle is a pair (B,t) where B is a 3-dimensional ball and t is a collection of n non-intersecting curves properly embedded in B. N-string tangles are formed by placing 2n points on the boundary of B, and attaching n non-intersecting curves inside B. Tangles, like knots and links, are studied through their diagrams. In the tangle model for DNA site-specific recombination, one is required to solve simultaneous equations for unknown tangles which are summands of observed DNA knots and links. This discussion will give a review of the tangle model including definitions. ## Date ## Fall 2015 Schedule October 5th Organizational Meeting October 12th Mentor and Mentee Meetup Every year, during the Hypatian Seminar we set up first years with older math graduate student mentors. We hope to see you there! November 2nd Title: Roundtable Discussion Topic: Teaching During the Hypatian Seminar we will have a round table discussion on teaching. Whether you feel like you don't quite know what you're doing in your weekly sections, or you have a lot of words of wisdom to share, you should come and join the dialogue! Chris Ograin and Stepan Paul will be joining us. ## Date ## Spring 2015 Schedule April 27th J.P. Serre’s lecture: How to write mathematics badly Organized by: Emily Macway and Massy Khoshbin Everyone at some point in their mathematical careers should see this video. If you haven’t already seen it, we highly recommend joining us to watch it together as a group. We will be following the video with a discussion about incorporating Serre’s key points into your own mathematical writing as well as sharing our experiences with reading others’ mathematical papers. May 4th Title: Crossed Modules of Racks Speaker: Alissa Crans, LMU A rack is a set equipped with two binary operations satisfying axioms that capture the essential properties of group conjugation and algebraically encode two of the three Reidemeister moves. We will begin by generalizing Whitehead's notion of a crossed module of groups to that of a crossed module of racks. Motivated by the relationship between crossed modules of groups and strict 2-groups, we then will investigate connections between our rack crossed modules and categorified structures including strict 2-racks and trunk-like objects in the category of racks. We will conclude by considering topological applications, such as fundamental racks. This is joint work with Friedrich Wagemann. May 18th Title: An introduction to Sage Speaker: Chris O'Neill, Texas A&M University We will explore the capabilities of Sage, a free, open source computer algebra system similar to Mathematica, Matlab, or Maple. Since its inception in 2004, Sage has come to be used by mathematicians around the world, and has many advantages over its commercial counterparts. No experience with Sage is assumed, and attendees are encouraged to follow along on their personal machines, either by preemptively installing Sage (http://sagemath.org/tour-quickstart.html) or by using Sage online through a web browser (https://cloud.sagemath.com/, no installation required). ## Date ## Winter 2015 Schedule January 12th CCUT Info Session Speaker: Molly Metz, CCUT We will have an info session for the Certificate in College and University Teaching (CCUT). This certification is designed for doctoral students who wish to demonstrate superior competence and experience in preparation for teaching at the university or college level. It is awarded in conjunction with a Ph.D degree, and looks great on your CV when you are applying for jobs. February 23rd Title: Inference of Functional Circadian Networks Speaker: Linda Petzold, UCSB In mammals, the Suprachiasmatic Nucleus (SCN), a brain region of about 20,000 neurons, serves as the master circadian clock, coordinating timing throughout the body and entraining the body to daily light cycles. The extent to which cells in the SCN can synchronize and entrain depends on the communication network between individual cell oscillators. Characterization of that network is challenging, due to the dynamics of the circadian oscillators and the stochastic noise inherent in discrete molecular chemical reactions. Statistical models based on information theoretic measures are well-suited for the analysis of stochastic information flow across networks. We have developed a methodology that uses information-theoretic measures on time course data to infer network structure, and tested its performance on data from computational models of networks of stochastic circadian oscillators with known connectivity. We then applied the method to experimental data, to infer the functional network for synchronization in mouse SCN slices. We will discuss the properties of the inferred networks. ## Date ## Fall 2014 Schedule October 13th Grad Students Mentor/Mentee Program Organized by: Amanda Curtis and Cindy Tsang In the last few years, Hypatian seminar has organized the mentor/mentee program, and we are going to do it again this year! It is going to be on next Monday (Oct 13) 3:30-4:30 in SH 6635. You can meet your mentor/mentee(s) there, and chat to get to know each other. And there will be baked goods! October 20th Panel Discussion Topic: How to Choose an Advisor Hypatian seminar will host a panel discussion on How to Choose an Advisor (or how to maintain a good working relationship with your advisor if you already have one) next Monday (October 20). 1) How do I decide which faculty I want to work with? 2) How do I know that I will work well with that faculty? 3) What are things that I should think about when choosing an advisor? A few experienced graduate students and Medina will be there to address these questions and any other questions that you have. It is extremely important that you pick an advisor whom you will enjoy working with!! October 27th Discussion: Math Circle and Talking to Non-Mathematicians Organized by: Michael Dougherty Hypatian Seminar will host a discussion on mathematical exposition for non-mathematicians. In particular, we will focus on our very own Math Circle, a weekly lecture for middle- and high-school students in the Santa Barbara area. I will give a short introduction to what Math Circle is and how you can get involved, followed by an informal discussion on exposing non-specialists (and younger students in particular) to interesting mathematics. November 10th Workshop on Work-Life Balance Led by: Turi Honegger, CAPS UCSB Stressed about your midterms, your student's miderms, your research and how to make them all work with your winter break and holiday plans? This week, the Mathematics Department's Hypatian Seminar will be hosting a discussion on work-life balance, lead by Turi Honegger of CAPS. A mix of viewpoints and experiences are welcome and encouraged. November 17th The Work of Maryam Mirzakhani Organized by: Sheri Tamagawa The Hypatian Seminar will give an overview of the work of Maryam Mirzakhani, the first female Field's Medalist! Courtesy of YouTube, we will watch talks about her award-winning research. November 24th Title: Stress management and reduction through leisure for graduate students Speaker: Michael Leitner College students are especially affected by stress. Brougham, Zail, Mendoza, and Miller (2009) report that: 1. During a typical semester, 52% of students experience high levels of stress. 2. Stress levels are related to cognitive deficits (poorer academic performance), illness, increased rates of depression and anxiety, decreased life satisfaction, higher consumption of junk food, lower rates of exercising, and a higher incidence of sleep problems. The problems with stress for college students in general are as common among graduate students as they are among undergraduates. Stress is a major factor contributing to the high percentage of Ph.D. students who complete all of their coursework but never complete their degree. The purpose of this seminar is to examine the relationship of leisure and stress and to explore how graduate students can use leisure to prevent or reduce stress. The learning objectives of this seminar are to: 1. Identify recreational activities that are positive stressors and those that are negative stressors. 2. Describe how recreational activity can be utilized to balance the stress quotient equation. 3. Explain the implications of type A/B research for leisure. 4. Define relaxation. 5. Identify recreational activities that can facilitate relaxation. 6. State a minimum of three personal leisure goals related to stress reduction. 7. To understand how to take control of stressors in your life and to make action plans for reducing the negative effects of these stressors. December 1st Title: Math courses for non-STEM majors Speaker: Lee Kennard In this talk/discussion, I will begin by sharing some of my experiences teaching non-calculus courses that fulfill quantitative reasoning requirements. Examples of topics for these courses include elementary graph theory, elementary number theory, set theory and cardinality, voting theory, or symmetry (in algebra, geometry, and real life). My goal here is to promote discussion on how best to run these courses, so I plan to leave ample time for discussion. December 8th Title: Symmetries, transformations, and groups of homeomorphisms Speaker: Katie Mann, UC Berkeley In many areas of mathematics, we try to understand a space by understanding its group of symmetries. In a first course in group theory, you learn that the symmetries of a regular n-gon are given by th dihedral group; later that the rotations of a sphere form a lie group SO(3); and even later (if you're lucky) that the modern idea of "doing geometry" comes from Felix Klein's idea to study a space by studying the algebraic structure of its group of symmetries. In my research, I study manifolds (surfaces, circles, 3-dimensional things, n-dimensional things...) by studying the algebraic properties of their transformation groups -- the group of all homeomorphisms or diffeomorphisms of the manifold. In this talk I'll give a mathematical tourist's introduction to this beautiful subject, which brings together techniques from geometry, dynamics, algebraic topology, and more. ## Date ## Spring 2014 Schedule March 31st Union Informational Meeting Speaker: Rob Ackermann As many of you may have heard, there is a scheduled unfair labor practices strike planned for Thursday, April 3rd. Rob Ackermann, who serves as our Campus Chair for the union, has graciously agreed to be available to give us more information about it. April 7th Panel Discussion Topic: How to Pass Quals Our panel of experts (1 professor + 3 grad students + possibly Medina) will share their tips and advice to help you SUCCEED. Attend this seminar, and you will feel less anxious and more prepared (psychologically, which will help you be more prepared mathematically) for the upcoming exams! April 14th Title: How to Give a Talk/Presentation Speaker: Michael Dougherty We will be discussing how to give effective math talks. I’ll share some of the things I’ve learned and we’ll end with a group discussion. We will cover the many different types of math talks and several strategies for preparing and giving them. April 21th Workshop: A crash course on using TikZ Led by: Ben Cote & Jon Lo Kim Lin This will be a bare-bones introduction to TikZ ist kein Zeichenprogramm (TikZ). More specifically, what is TikZ? Basic examples include: graphic functions in the plane, commutative diagrams (Snake lemma), flow charts and TikZ libraries (Koch flakes). We encourage everyone to bring their laptops. ## Date ## Winter 2014 Schedule January 13th Networking Organized by: Maree Jaramillo Hypatian Seminar welcomes everyone to the new quarter! To kick it off, our first event will be centered around the theme of NETWORKING. Since we figure there is no better way to work on networking than to do it, Hypatian Seminar cordially invites EVERYONE to come for some light refreshments (FREE FOOD!) at our normal seminar time and place. This casual event should be a nice opportunity to work on your networking skills, or share any sage advice you've gained over the years. January 27th Workshop on Making a Website Led by: Matt Porter Did you ever want to have your own website, but then realized that would require making a website? On Monday in Hypatian Seminar we'll look at how to relatively painlessly get a pretty good website up and running in no time (or how to make the website you have better). February 3rd An Informal Discussion: What is institutional bias? Led by: Amanda Curtis and Michael Dougherty We’ll be hosting an open discussion on institutional bias in the Hypatian Seminar today. Please feel free to stop by to share your experiences and discuss ways we can improve our own environments! February 10th Panel Discussion Topic: How to do Research? A few of the post-docs, each from a different field, have kindly agreed to share their experience and advice on doing research. If you are wondering what it is like to do research, or want to get better at it, or just want some **free delicious cookies**, then you should join us! Whether you are still in the early stage of grad school, or graduating soon, I am sure you will be able to benefit from this seminar. February 24th Title: How to find a parking spot and other combinatorial pursuits Speaker: Amanda Ruiz Imagine a one-way cul-de-sac with four parking spots. Initially they are all free, but there are four cars approaching the street, and they would all like to park. To make life interesting, every car has a parking preference, and we record the preferences in a sequence of four numbers; e.g., the sequence (2, 1, 1, 3) means that the first car would like to park at spot number 2, the second and third drivers prefer parking spot number 1, and the last car would like to part at slot number 3. The street is very narrow, so there is no way to back up. Now each car enters the street and approaches its preferred parking spot; if it is free, it parks there, and if not, it moves down the street to the first available spot. We call a sequence a parking function if all cars end up finding a parking spot. For example, our sequence (2, 1, 1, 3) is a parking function, whereas (1, 3, 3, 4) is not. Naturally, we could ask about parking functions for any number of parking spots; we call this number the length of the parking function. A moment's thought reveals that there is one parking function of length 1, three parking functions of length 2, and sixteen parking functions of length 3. A beautiful theorem due to Konheim and Weiss says that there is a pattern to be found here: there are precisely (n+1)^{n-1} parking functions of length n. We will hint at a proof of this theorem and illustrate how it allows us to connect parking functions to seemingly unrelated objects, which happen to exhibit the same counting pattern: a certain set of hyperplanes in n-dimensional space first studied by Shi, and a certain family of mixed graphs, which we introduced in recent joint work with Matthias Beck, Ana Berrizbeitia, Michael Dairyko, Claudia Rodriguez, and Schuyler Veeneman. March 3rd Title: How to Write a Teaching Philosophy Statement Speaker: Kim DeBacco Writing a Teaching Philosophy Statement can be a challenge, and is required for most faculty positions. At the same time, examining and articulating your teaching philosophy can help you to become a more effective teacher. You will work through a series of reflective exercises, and you will leave the workshop with a draft and outline of your teaching philosophy statement. March 10th Title: How to run a more dynamic discussion section without really trying (harder). Speaker: Arielle Leitner and Elizabeth Thoren Imagine only spending less than an hour each week to prepare a full day of engaging section meetings that leave you feeling satisfied with your teaching! TAs, do you spend hours preparing for sections that only seem to fall flat? Do you feel like your brain is going to fall out of your head after running 4 sections in a row? Are your students distracted? confused? missing section all together? We have suggestions for avoiding these problems and more. You can spend less time preparing for (and recovering from) a full day of section meetings if you plan ahead in the right way. We will workshop planning dynamic discussion section activities more efficiently. ## Date ## Fall 2013 Schedule September 30th Title: Responding to Distressed Students Angela Andrade the Associate Dean of Wellness Services and Director of Student Mental Health Coordination Services along with a few members of the Student Behavioral Intervention Team will provide attendees with a context for student mental health, to introduce and review the distressed student protocol and appropriate campus resources for students,offer suggestions on how to refer students, and review potentialdistressed student scenarios. October 7th Mentor/Mentee Mixer Organized by: Kate Hake and Amanda Curtis October 14th Funding Workshop Led by: Colleen Delaney November 18th Title: N/A Speaker: Chris Nowlin Chris Nowlin will be speaking on what its like to work for the NSA. November 25th Title: Preparing Your CCUT Portfolio Speaker: Dr. Kim DeBacco, Instructional Development The Certificate in College and University Teaching (CCUT) is designed for graduate students who wish to demonstrate experience and superior competence in preparation for teaching at the university or college level. The requirements include completion and attainment of a number of teaching-related skills and experiences (including TAships, TA trainings, pedagogy courses), culminating in independent instruction of an entire course (as a Teaching Associate) with the support of a UCSB faculty mentor. This session will begin with an overview of the drafting, submission and portfolio evaluation process. December 2nd Title: CV Workshop Speaker: Michael Dougherty We’ll be discussing the elements of a good CV and what it can do for you. I will give a short overview of how to build and edit a CV, followed by an open workshop and discussion. If you currently have a CV, feel free to print off a copy to bring along and get feedback from your peers. ## Date ## Spring 2013 Schedule April 8th Panel Discussion Topic: How to Pass Qualifying Exams Hypatian Seminar will be hosting a panel on how to pass your quals. Our panel of experts will share their tips and tricks to help you SUCCEED. If you share our crippling fear of missing out on fun (and baked goods!), be sure to attend! April 15th Panel Discussion Topic: Becoming a Teaching Associate you ever considered working as a teaching associate while at UCSB? Maybe you are curious about the process of becoming one, or what the advantages of becoming one might be? Do you have more questions than those I have posed here? Join us for Hypatian Seminar this Monday, where a panel of experts will answer any questions you might have. This should prove to be informative and perhaps even motivating; we hope to see you there! April 22th Funding Workshop Led by: Ester Trujillo This Monday, the Hypatian Seminar will feature a talk from our Graduate Division Funding Peer Advisor, Ester Trujillo. This workshop will include an overview of UCSB graduate student funding resources including UC awards, Extramural awards, and Financial Aid. We will create searches so having a computer nearby will be extremely useful. We will also review department-specific award listings. If getting paid to learn sounds like a sweet gig to you, please join us on Monday April 22 in room 6635 at 3:30pm. See you there! April 29th Panel Discussion Topic: Job Search Whether you are in your first year, going on the job market soon (yikes!!), or anywhere in between, if you are interested getting a job in academia then this panel is for you. Feel free to bring questions about any part of the process (or academic jobs in general!) that you may be curious about. This panel will be at the usual place and time (SH 6635, 3:30 pm). May 6th Title: Mentoring Undergraduate Research in Mathematics Speaker: Diane Hoffoss Have you ever wondered what things count as undergraduate research in mathematics? how to find good research problems for undergraduates? how to find interested students? what support/funding you can expect for mentoring undergraduate research? At this talk, we will discuss some answers to these questions and more from the point of view of a liberal arts university professor. Please bring your own questions as well to make for a livelier conversation! May 13th Title: Writing Mathematics Speaker: Daryl Cooper I will give a somewhat personal perspective on the difference between good and bad mathematical writing, thinking and talking. May 20th Title: Some of the Best Advice I've Received Speaker: Alissa Crans My career trajectory has been anything but traditional. I accepted a tenure-track offer at Loyola Marymount University immediately after finishing my PhD, then went on leave twice to take postdoctoral positions at The Ohio-State University and the University of Chicago. After earning tenure, I participated in the sabbatical program at the NSA and am currently the Director of Educational and Outreach Activities at the MSRI (Mathematical Sciences Research Institute) in Berkeley, CA. None of this would have happened without great advice, support, and encouragement I've received along the way from my thesis advisor, mentors, parents, and even my high school band director! I'll share some of this advice and am very happy to answer any questions about my background or experiences. June 3rd Informal Roundtable Topic: Advice from the Graduating Class Hypatian seminar is hosting an informal roundtable for the graduating class. We will celebrate their graduation and they will share their advice about grad school,research, job search, etc. There will be delicious cakes baked by Arielle and non-Lipton tea. ## Date ## Winter 2013 Schedule January 14th Panel Discussion Topic: How to Choose an Advisor We are starting off the quarter with a panel on choosing an advisor. Join us to hear from experienced graduate students. January 28th Inkskape Workshop Led by: Laura Plunkett (Zirbel) and Pat Plunkett Do you want to learn how to create awesome figures for papers, talks, and other documents? Then this is the workshop for you! In this workshop, we will be learning the basics of Inkscape and about the world of scalable vector graphics, why they rock, and how to include them into a LaTeX document. This will be a workshop, so if possible bring a laptop with the software already installed; we will be going through a step-by-step process of creating an image and inserting it into LaTeX. February 4th Online Math Lab Information Session Led by: Stepan Paul and Michael Yoshizawa The Online Math Lab is a website that provides links to internet resources for students enrolled in our lower division math classes. We are giving this talk to let faculty and TA's know about the site and how they can publicize it as a resource for students seeking extra help. Links have been pre-screened to match with a specific course's syllabus and, currently for 34AB, we've also added links to relevant sections of the site on the student's Webwork problems. We'll demo the site and show how faculty can access the modified 34AB Webwork problems containing the links. We're also looking for feedback on how to improve site. February 11th Title: Helping Students take Responsibility for their Mathematics Learning Speaker: Lisa Berry Do you find yourself lamenting about students' lack of motivation, poor work ethic or their all-consuming focus on getting "the correct answer?" If so, this seminar will provide you with concrete strategies to overcome these impediments to learning. We will discuss grading strategies that can revitalize students' motivation to engage with the homework, ways to structure your lecture/section to involve students, and feedback mechanisms to help foster a shared responsibility for learning. This focus on "student-centered learning" will be a useful framework for those of you who plan to complete the Certificate in College and University Teaching (CCUT program). March 4th Organizational Meeting March 11th Title: A Presentation of$SL(2,\Z[i])$in two different ways Speaker: Brie Finegold I'll talk about a classical way from the 1960's to derive a presentation for the special linear group over the Gaussian integers by viewing it as a group acting on the Hyperbolic plane. Then I'll talk about my way to find a presentation of the group by viewing it as acting on a variation on the curve complex of a torus. The talk will be interactive and compare and contrast the two methods. March 28th Panel Discussion Topic: Mathematics in Industry Have you ever wondered what it would be like to be a mathematician working in industry? Or what it even means to be a mathematician in industry? Perhaps you're just curious to see what it might be like to transition from academia into industry. Come and find out this and more at next week's Hypatian Seminar!! We are pleased to be hosting a panel of professionals working here in the Santa Barbara area who have graciously agreed to answer the questions you might have have regarding math and industry. They will each offer their own unique perspective on what it is like to work in industry currently. Our guest panelists include: Gaemus Collins (Toyon), Dana Iltis (Warren & Selbert), Robert Sulway (RightScale), Briana Tippets (Toyon). ## Date ## Fall 2012 Schedule October 1st Hypatian Tea Graduate Mentor Meet and Greet Organized by: Arielle Leitner and Maree Jaramillo. Please join us on Monday, October 1 at 3:30-4:30 pm in SH 6635 for tea and baked goods. Everyone is invited to this event that will be a time for mentors and mentees to meet, and for fun to be had by all. October 8th, 15th How to Build a Website Workshop Led by: K. Grace Kennedy and Laura Plunkett Bring your laptops! We are going to learn how to build our own websites. We will discuss: -how to create your website (including needed technology), -what kind of information you can/should/might include as a first year, fifth year, and anything in between -how to make your web page user friendly, -what kinds of features you can include, -how to upload it to the math server (i.e. let everyone see it), and -how to do this as quickly and easily as possible. Part of the seminar will be workshop so that you have time to create something. We hope that by the end of this Monday everyone will have a basic template for their website declaring "Hello world!" that they can add onto in the following week. On the second Monday, the 15th, we will have an open workshop. Several website-savy grad students and Marcel, our tech ninja, will be around to help. Here are some useful links and notes from our meeting: HTML/CSS templates Skillcrush Information Sheet October 22th Panel Discussion Topic: Applying to Graduate School Panel Have questions about graduate school in mathematics and the application process? Come to Hypatian Seminar on Monday, October 22nd to have your questions answered by a panel of UCSB graduate students who have recently been through the process. October 29th Panel Discussion Topic: Doing Math abroad Join us to discuss doing mathemtics while abroad with Arielle Leitner (Israel), Stepan Paul (Japan), Michael Yoshizawa (Japan), and K. Grace Kennedy (Wales/Iceland). November 5th Title: Heegaard splittings of 3-manifolds Speaker: Marion Moore Campisi We will discuss various ways to visualize 3-manifolds and decompose them into simple pieces. November 19th CV Workshop Led by: Michael Dougherty Whether you've had one for years or you're just getting started, a CV is essential for everyone. In this workshop, we'll discuss - Why you need a CV, - What you should include, - And how to make it look awesome. If you don't have a CV, no worries! If you do, bring it along for a brief workshop following the discussion. ## Date ## Spring 2012 Schedule April 9th Title: Flocking, phase transitions, and associated PDEs Speaker: Alethea Barbaro, UCLA Agent-based models are an increasingly important tool for mathematicians working in interdisciplinary mathematics, since they are highly flexible and easily explained to researchers in fields as diverse as physics, biology, criminology, psychology, computer science, and economics.Ê These types of models include both lattice and off-lattice models, and often exhibit interesting complex dynamics such as flocking behavior and phase transitions.Ê Recently, these models have also spawned an exciting and active area of research in mathematics by the derivation and analysis of associated kinetic and hydrodynamic PDEs.Ê In this talk, I will discuss my work on fish migration, gang territorial development, and flocking behavior and the analysis of associated systems. April 16th Union, Health Care, and TA Rights Information Session Led by: Rob Ackermann and Filiberto Nolasco Come learn about our graduate student health care, our rights as TAs, and about the union in general. As you may or may not know we are on a new healthcare plan called 'UCShip' this year. Bring questions! April 23rd Title: Variational methods for image reconstruction and parameter identification, AC, UCM Speaker: Ana Maria Carpio Rodriguez, Universidad Complutense Madrid A common strategy for finding multiple scatterers buried in a medium consists in illuminating the medium with some type of radiation. The emitted wave interacts with the medium and the objects, and the resulting wave field is measured at a number of receptors. Knowing the measured data, we would like to locate the objects and determine their material properties. Variational methods aim to reconstruct objects by finding domains and parameters which minimize appropriate constrained cost functionals. In simple problems of acoustic or electromagnetic scattering, the incident radiation is time harmonic and the constraints of the cost functionals are transmission problems for Helmholtz equations. We propose a descent strategy which provides detailed approxima tions of the geometry of the obstacles and their material parameters in few steps and with scarce data, without any a priori information. Initial guesses, and successive corrections of the domains are constructed using the topological derivative of the functional. The number, size and location of the objects are correctly approximated in the iterative procedure. Small scatterers and obstacles with holes are detected. Approximations for the material parameters of the different objects are found by a gradient technique that can detect spatial variations. Similar ideas may be used in acoustic or electromagnetic scattering problems involving more complex constraints, in photothermal imaging with thermal waves or in electrical impedance tomography. April 30th Organizational Meeting May 14th Informal Roundtable Topic: Last year of graduate school Are you wondering what your last year at UCSB will be like? Join us for an informal roundtable with this year's graduating class. We'll discuss the ins and outs of finishing your dissertation while managing the job search and answer all of your nagging questions. Coffee and goodies provided by Hypation seminar. For more on the topic, check out Laura Zirbel's blog on preparing for your last year in math grad school: http://mathgradblog.williams.edu/year/ May 21st Panel Discussion Topic: Applying for an Academic Job We have compiled a terrific panel of experts with experience on both sides of the job search to answer your questions. Panelists include Alethea Barbaro (UCLA), Michael Gagliardo (California Lutheran University) and our own Marty Scharlemann. Job seekers should also check out the AMS webpage Advice for New PhDs - they have links to blogs, pdfs and websites covering everything from the job search to managing the first few years of your budding academic career. ## Date ## Winter 2012 Schedule January 30th Title: Effective Strategies for Teaching Math: Beyond the Usual Formulas Speaker: Lisa Berry, UCSB Have you ever felt frustrated that your students "just aren't getting it," despite your best efforts to explain mathematical concepts and work through problems? This talk will explore underlying causes that may explain why students in a typical math course/section tend to fall short of mastering the course learning goals. We will investigate alternative teaching strategies that can help students to succeed, including the importance of context, attention to units, and active learning approaches. Participants will be invited to join in the conversation and can expect to leave with new ideas for their teaching. February 13th Title: An introduction to Operad theory Speaker: Marcy Robertson, The University of Western Ontario An operad is an abstraction of a family of composable functions of$n$variables. Indeed, the most fundamental example of an operad is the endomorphism operad$End_X :=\{ Map(X^n,X)\}_{n≥1}$. Where, given a set or topological space$X$, \{Map(X^n,X)\}$ means the set or space of functions from the$n$-fold product of $X$ with itself to $X$, together with the operations $Map(X^n,X)\times Map(X^m,X)\rightarrow Map(X^{n+m−1},X)$ given, for $1 ≤ i ≤ n$, by $(f\circg)(x_1, ... ,x_{m+n−1}) = f (x_1, ... , x_{i−1}, g(x_i , ... , x_{i+m−1}), x_{i+m},...).$ Operads were originally studied as a tool in algebraic topology, but the theory of operads has recently received new inspiration from homological algebra, algebraic geometry, and especially string field theory and deformation quantization. The purpose of this talk is to introduce the basic definitions and examples of operad theory and to describe as many applications as time permits.

February 15th (Wed)

Work-life balance: a workshop for women in science

Presented by: Tracy Blois, Ph.D., President of the Los Angeles - Ventura Chapter of the Association for Women in Science (AWIS)

The UCSB Women in Science and Engineering (WISE) organization is putting on this exciting workshop for women in science. Take a look at the flyer. Make sure to RSVP.

February 27th

Title: A game based on knot theory

Speaker: Ayaka Shimizu, Osaka City University Advanced Mathematical Institute (OCAMI)

We introduce "Region Select" which is a game (or game app) using knot theory. In this game we consider a knot projection on a display whose crossings have "lamps" which can be turned on or off by clicking on the region bordering it. The goal of this game is to light up all of the lamps by clicking on regions. In this talk, we show that we can complete the game for any knot projection with any state of lamps by considering "region crossing change" which is a local move on knot diagrams. This game is a joint work with Akio Kawauchi and Kengo Kishimoto.

Play Region Select!
Get Region Select for your android!

March 12th

Panel Discussion

Topic: Qualifying Exams

## Fall 2011 Schedule

September 26th

Title: The salesman with marital problems and other questions about graphs

Speaker: Maggy Tomova, The University of Iowa

The traveling salesman problem is an old question that has been studied by mathematicians for almost a century. The question can be formulated as follows: Given a number of cities and the time to get from one city to another, what is the fastest route for a salesman to take so he visits all cities?

In this talk we will consider the exact opposite of this problem. Suppose the salesman wants to stay on the road for as long as possible. What is the best way to achieve this goal? We will show how to model this problem with graphs and solve it for certain families of graphs.

October 3rd

CCUT and coffee

Led by: Kim McShane-DeBacco

Join us for coffee at Nicolletti's and a discussion about CCUT, College Certificate in Undergraduate Teaching. Kim McShane-DeBacco will lead the discussion. She is an Instructional Consultant here at UCSB. CCUT is an great program that UCSB offers to help prepare graduate students to teach at the undergraduate level.

October 10th

Title: An introduction to Claire's Ph.D. thesis and its generalizations

Speaker: Claire Levaillant, UCSB

I will define the Birman-Murakami-Wenzl algebra abbreviated "BMW algebra", both in terms of algebraic relations and in terms of diagrams. I will show to you how I build a representation of the BMW algebra of type $A_{n-1}$ which is also a representation of the braid group on $n$ strands. The BMW algebra is based on two parameters. I will explain how I find complex values of the parameters for which the algebra is not semisimple. These values depend on $n$, where $n-1$ is the number of generators of the BMW algebra of type $A_{n-1}$ and also the number of generators of the braid group on n strands. I will then tell how I generalize this work to Coxeter type $D_n$. My talk at the topology seminar will be about type $E_6$ and you should then be finely prepared to understand it.

October 17th

Title: Rational Points and Hypergeometric Functions

Hypergeometric functions seem to be ubiquitous in mathematics, particularly when counting rational points over finite fields. In this talk, we will show that the number of points over a finite field Fq on a certain family of varieties is a linear combination of hypergeometric functions. We will also give a brief introduction to working with p-adic numbers and use results by Koblitz and Gross to find explicit relationships. Finally, we will explain how these formulas could be useful for computing Zeta functions in the future and in extending some classical results in number theory.

October 24th

Title: Knot complicated

Speaker: Abigail Thompson, UC Davis

I'll talk about various methods of measuring how "complicated" a knot (like a knotted loop of string) is, and how much is known about each measurement for a few standard knots. I'll also talk about physical methods of sorting out knots, such as by gel electrophoresis. Finally I'll describe some preliminary results from a research project completed with a group of undergraduates at UCD, in which we found a good macro-scale method that seems to sort knots (made out of spaghetti)(seriously) in a manner similar to gel electrophoresis for knotted strands of DNA.

October 31st

Informal Meet and Greet with Undergraduates

November 7th

Title: Introduction to mathematical models of earthquakes and an application to the interseismic period

Speaker: Brittany Erickson, Stanford

With the goal in mind of modeling earthquake rupture, we will start by establishing a model of how the solid earth responds to an applied force. Momentum balance with Hooke's law for the stress-strain relationship yields the elastodynamic wave equation. Plane wave solutions result in an eigenvalue problem with three eigenvectors corresponding to one longitudinal p-wave and two shear waves. We will then look at a 2-d example of the wave equation known as the anti-plane problem where a fault lies on the boundary of the elastic medium. The seismogenic zone along the fault is governed by a friction law, and the system is loaded by imposing steady creep on the down-dip extension of the fault. At the surface of the earth, the corners of the domain can potentially have incompatible boundary conditions which can be problematic computationally. Summation-by-Parts finite difference operators have many desirable properties including weak enforcement of boundary conditions through the Simultaneous Approximation Term. As a simple illustration we will onsider this method applied to the one-way wave equation. Finally, my postdoctoral work has been the development of a time-stepping algorithm to account for quasi-static evolution in the interseismic period prior to an earthquake. We will discuss this idea in the anti-plane problem context to show how cycles of earthquakes can be simulated with corresponding slip velocities ranging over 10 orders of magnitude.

November 14th

Panel Discussion

Topic: Advancing to Candidacy and Beginning Research

November 21st

Title: Introduction to bridge presentations of links

Speaker: Yeonhee Jang, Hiroshima University

This will be an introductory talk on my research, mainly on bridge presentations of links. We recall the definition and basic properties of bridge presentations of link, and I will introduce briefly studies on bridge presentations of links so far.

November 28th

Organizational Meeting

## Spring 2011 Schedule

April 4th

Title: Stability of Vortex Patches

Speaker: Elizabeth Thoren, UCSB

I'll introduce vortex patch solutions to Euler's equation for incompressible fluids (think hurricanes). Then we'll discuss how the conservation of certain quantities in Eulerian fluid flow leads to a nice stability result for circular patches.

April 11th

Panel Discussion

Topic: How to do research

This week, we will be discussing the process of doing research. We will have on the panel distinguished researchers to share with us their experiences. Please join us and bring questions and/or comments!

April 25th

Title: Lattice Models of Polymer Entanglements

Speaker: Chris Soteros, University of Saskatchewan

Self-avoiding polygon models have been used to study ring polymers(long closed chain molecules) in dilute solution for over 50 years. For such models, a vertex of the polygon represents a monomer unit and an edge of the polygon joins two monomer units which are chemically bonded together in the polymer. Distinct self-avoiding polygons on a lattice, such as the simple cubic lattice, are used to represent distinct conformations of a ring polymer. At equilibrium in dilute solution, each equal-length polygon is considered to be equally likely as a polymer conformation, and one is interested in the average spatial properties of the polymer as a function of its length. For example, there is much interest in their entanglement complexity (e.g. probability of being knotted), especially with respect to modelling enzyme action on circular DNA.

In this talk, I will review why polymer entanglements are of interest; then introduce the self-avoiding polygon model for ring polymers described above; and finally give an overview of some of the theoretical and numerical approaches for studying polymer entanglements with this model.

May 2nd

Title: Signed minor-minimal intrinsically linked graphs in RP^3

Speaker: Yen Duong

Graph theory, knot theory, and combinatorics combine in a talk in which we classify graphs that contain two linked cycles regardless of their embedding in RP^3.  First we explore what intrinsic linking means, then we find graphs with this quality, and finally we prove that we've found all of them.  This presentation is from my REU at SUNY Potsdam in 2009 and is very accessible. (Yen)

Conjugacy Tests in the Nottingham Group (Teddy)

Speaker: Teddy Einstein

Let K be a field of characteristic p. We study conjugacy of elements of the Nottingham group over K, $N(K) = t+t^2 K[[t]]$, a group of formal power series under composition. We will give a brief overview of the basic properties of the Nottingham group and some of the tools used to work with the Nottingham group. We use these tools to exhibit a test for conjugacy of torsion elements with order p developed by Benjamin Klopsch. Finally, we will present an original result generalizing the conjugacy test to elements which have a common p-th iterate. (Teddy)

May 9th

Title: Geometric Methods in Group Theory

Speaker: Kim Ruane, Tufts

In this talk we will see how to prove two standard facts from group theory using geometric methods. The first is about the symmetric group - a group most students come in contact with in an undergraduate abstract algebra course. We will prove the standard fact that each permutation can be assigned a label of "odd" or "even" in a well-defined way using the structure of a Cayley graph for this group. The second is about finitely generated free groups. We will prove that any nontrivial finitely generated normal subgroup of such a group is finite index. Again we will use the geometry of a Cayley graph to do the proof.

May 16th

Title: Experts' Representational Knowledge of Division of Fractions

Speaker: Ani Dzhidaryan, UCSB

The topic of fractions, and more specifically the division of fractions, remains to be one of the more challenging topics that both students and teachers grapple with. Recently, studies have suggested that the number line may serve as a representational tool that can help foster better understanding of this topic. Yet, in a complimentary study, we have found that teachers struggle with constructing a number line to represent division of fractions and would initially attempt to use an area model. In this exploratory study, we examined whether graduate students and professors within the math and physics departments would spontaneously see and use a number line when asked to visually represent division of fractions. Our results seem to suggest an initial preference for the area model, but our informants possessed the ability to construct a number line model when prompted to do so. Cross-national comparisons of teachers' and experts' representational preferences may further clarify whether the preference for the area model arises as an artifact of cultural practices (e.g., teaching practices) or is indicative of a more easily retrieved cognitive model.

May 23rd

Title: An Introduction to Contact Geometry

Speaker: Joan Licata, Stanford

Contact geometry studies odd-dimensional manifolds equipped with some extra geometric structure. An active area of research, this field has connections to low-dimensional topology, Hamiltonian mechanics, and parallel parking. In this talk, I'll introduce some definitions and interesting examples, focusing particularly on the knot theory associated to contact three-manifolds.

## Winter 2011 Schedule

January 19th (Wed)

Titles: Zero-divisor graphs, cut-sets, and maximal ideals

Speaker: Ben Cote

A zero-divisor graph is a graph whose vertices are all the nonzero zero-divisors of a finite commutative ring R. Two vertices a and b are connected by an edge if and only if ab=0. C. Ewing, M. Huhn, C. M. Plaut, D. Weber and I examined minimal sets of vertices which, when removed from a zero-divisor graph, separate the graph into disconnected subgraphs. We classified these sets for the zero-divisor graphs of all finite commutative rings with identity. I will be presenting a few standard results about zero-divisor graphs along with our results.

Title:Solving Polynomials for Profit

Megan Maguire

I will talk about the XL family of algorithms that attempt to break block ciphers (such as DES, and SAES) by modeling these ciphers as a system of multivariate polynomials. I will define mutant polynomials, and talk about how exploiting them might or might not lead to an improvement of the XL algorithm.

January 31st

Title: The Development of Mathematical Knowledge for Teaching in Preservice Teachers: A Comparative Study

Speaker: Bill Jacob, UCSB

The purpose of this presentation is to present results from of a design research study that explored the development of early "mathematical knowledge for teaching" (MKT) in undergraduates. Prospective elementary and secondary teachers participated in this study while enrolled in mathematics courses that blend mathematical content with the examination of the mathematical development of learners as evidenced in case studies. Part of the presentation will introduce the tools used in qualitative research in mathematics education and the second part will describe the research, which deals with the collegiate mathematics preparation of future K-12 teachers. This research is joint with Sarah Hough, Kyunghee Moon, and Monica Mendoza.

February 7th

Title: Viral entry into cells

Speaker: Maria-Rita RD'Orsogna, California State University Northridge

Successful viral infection of a healthy cell requires complex host-pathogen interactions. In this talk we focus on the dynamics specific to the HIV virus entering a eucaryotic cell. We model viral entry as a stochastic engagement of diffusing receptors and coreceptors on the cell surface. We also consider the transport of virus material to the cell nucleus by coupling microtubular motion to the concurrent biochemical transformations that render the viral material competent for nuclear entry. We discuss both mathematical and biological consequences of our model, such as the formulation of an effective integrodifferential boundary condition embodying a memory kernel and optimal timing in maximizing viral probabilities.

February 14th

Panel Discussion

Topic: How to find an advisor

February 28th

Special Colloquium with the Algebra Seminar

Part 1: Planar networks, determinants, and generalizations
Classical work provides an elegant relationship between determinants and path counting in acyclic directed graphs. This approach led to a complete combinatorial description of totally positive matrices. We will look at this elementary construction and explore several ways to extend beyond the class of totally positive matrices.

Part 2: A combinatorial description of the totally nonnegative Grassmannian
The totally nonnegative Grassmannian is the subset of the Grassmannian in which all Plucker coordinates have the same sign. As with totally positive matrices, it is possible to provide a parametrization using certain weighted planar graphs. We will give combinatorial formulas (in both directions) for a bijection between points in the TNN Grassmannian and these special graphs.

March 7th

Panel Discussion

Topic: How to pass the quals

## Fall 2010 Schedule

October 4th

Panel Discussion

Topic: Technology in the Classroom

At 3h30 in SH6635, there will be a panel discussion on use of technology in the classroom and as a teaching tool. Daryl Cooper, Julia Galstad, Rahul Shah, and Laura Zirbel will be giving 5-10 minute introductions to their pet technologies followed by a Q&A session. Fuz Rogers will also be present on the panel to answer technical questions.

Daryl Cooper will be speaking about his innovative use of i>clickers in Math 34A. This simple tool has a wider range of use in the classroom than most people realize. There will be i>clickers for you to try.

Julia Galstad will demonstrate a few free online math apps that can make teaching more fun for instructors and students.

Rahul Shah will be speaking about our Graduate Resource Sharing site on Gaucho space that he set up with Sonja Mitchell last year. This is a file share on Gaucho Space where graduate students can load up anything that might help their fellow graduate students: old quizzes for teaching, worksheets, study guides, and also qualifying exam solutions.

Laura Zirbel will speaace- how to set up a course page, utilize all of the features, and why it is so great and worth the initial investment to fking about Gaucho Spigure it out.

Bring your laptops if you want to play along.

October 18th

Title: An Introduction to Geometric Group Theory

Speaker: Tara Davis, Vanderbilt University

FAs graduate students, we often hear about our professors research interests: algebraic number theory, representation theory, geometric group theory, etc. However, at least at the beginning of our careers, we have little idea of what doing research in these areas would actually entail. This talk will serve as an overview and introduction to the area of geometric group theory. We will explain how to view a finitely generated group as a geometric object. We will also introduce some of the specific topics of interest in this field. (First talk)

We study the effects of subgroup distortion in the wreath products A wr Z, where A is finitely generated abelian. We show that every finitely generated subgroup of A wr Z has distortion function bounded above by some polynomial. Moreover, for A infinite, and for any polynomial, there is a 2-generated subgroup of A wr Z having distortion function equivalent to the given polynomial. If A is finite, then every finitely generated subgroup in A wr Z is undistorted. (Second talk)

October 25th

Panel Discussion

Topic: The Two-Body Problem

Come and listen to established professors discuss their experience finding jobs in academia together with their partners. We will have our very own Jon McCammond of the UCSB math department and his partner Mary Bucholtz of the linguistics department. We will also have Rena Levitt, who is currently a Visiting Assistant Professor at Claremont McKenna College. She (and her husband John) graduated from the UCSB Math department in 2008.

November 15th

Title: Mathematical approaches to modeling cancer treatments.

What can mathematics tell us about the treatment of cancer? In this talk I will present some of work that I have done in the modeling of tumor growth and treatment over the last ten years.

Cancer is a myriad of individual diseases, with the common feature that an individual's own cells have become malignant. Thus, the treatment of cancer poses great challenges, since an attack must be mounted against cells that are nearly identical to normal cells. Mathematical models that describe tumor growth in tissue, the immune response, and the administration of different therapies can suggest treatment strategies that optimize treatment efficacy and minimize negative side-effects. However, the inherent complexity of the immune system and the spatial heterogeneity of human tissue gives rise to mathematical models that pose unique analytical and numerical challenges. In this talk I will briefly discuss two mathematical problems that we have encountered in our work: optimization of systems of delay differential equations, and the analysis of spatial models that incorporate different time scales.

No knowledge of biology will be assumed.

November 20th

Special Event: 3rd Annual Women in Mathematics Symposium at Pomona College

Hypatian Seminar is funding 14 women from UCSB to go to the 3rd Annual Women in Mathematics Symposium at Pomona College including 9 talks. Take a look at the abstracts.

November 29th

Film Watching

Title: Agora

Agora is a 2009 movie about Hypatia of Alexandria, our patron mathematician. It is set in 4th century Roman Egypt and is classified as historical fiction. Here is a review by the Los Angeles Times.

## Winter 2010 Schedule

January 4th

No seminar

WEDNESDAY 3:30-4:30 in South Hall 6635
Amanda Beeson UCSD
Recently graduated from UCSD, Dr. Beeson is a candidate for a position here at UCSB. Her research is on "Maximal Almost Abelian Extensions".

THURSDAY 3:30-4:30 PM South Hall 6635
Lillian Pierce Institute for Advanced Study at Princeton
Originally from California, she recently earned her doctorate from Princeton this last year studying "Discrete Analogs in Harmonic Analysis".

January 11th

Title: Mathematical Anecdotes and Jokes

Speaker: Laura Zirbel, UCSB

Historical anecdotes and jokes can make any subject material engaging and dynamic. Mathematics has an exceptionally bizarre cast of characters including the insane, gamblers, blind geniuses and cults.

The first part of this talk will be a Jeopardy style competition, followed by an informal exchange of our favorite material for undergraduate classes, as well as those stories we'll find any excuse to tell.

January 20th (Wed)

Title: Discrete Stochastic Simulation of Spatially Inhomogeneous Biochemical Systems

Speaker: Linda Petzold, UCSB

In microscopic systems formed by living cells, the small numbers of some reactant molecules can result in dynamical behavior that is discrete and stochastic rather than continuous and deterministic. An analysis tool that respects these dynamical characteristics is the stochastic simulation algorithm (SSA), which applies to well-stirred chemically reacting systems. However, cells are hardly homogeneous! Spatio-temporal gradients and patterns play an important role in many biochemical processes. In this lecture we report on recent progress in the development of methods for spatial stochastic and multiscale simulation, and outline some of the many interesting complications that arise in the modeling and simulation of spatially inhomogeneous biochemical systems.

Location change: South Hall 5607F (The PSTAT department)

January 25th

Title: Hyperbolic Surfaces: An introduction

Orientable 2-dimensional manifolds are rich in mathematical structure. They connect complex analysis with geometry and group theory. A large subcategory of orientable 2-manifolds consists of those that admit a Riemannian metric with constant curvature -1; i.e., hyperbolic surfaces. The first half of the talk will cover the basic geometry of 2-dimensional hyperbolic space viewed as a subset of the complex plane. In the second half, we will explore the correspondence between hyperbolic surfaces and discrete groups of hyperbolic isometries. This is the first in a series of talks. The second talk will take place in the Discrete Geometry Seminar on January 27.

February 1st

Title: The homology of finite dimensional algebras

Speaker: Birge Huisgen-Zimmermann, UCSB

We will start with examples of finite dimensional algebras, placing special emphasis on path algebras of quivers (= finite directed graphs) modulo relations. Then we will introduce projective dimensions of modules over such algebras, again illustrated by examples. In particular, we will encounter a graphical method for computing projective dimensions in certain examples encountered earlier.

February 8th

Title: The homology of finite dimensional algebras, part II

Speaker: Birge Huisgen-Zimmermann, UCSB

A continuation from the talk last week.

February 17th (Wed)

Title: Objective and Subjective Decision Factors: Modelling Consumer Behavior from Individual to Population Scale

Speaker: Monica Gabriela Cojocaru, visiting professor at UCSB

Modelling human decision processes and their impact on everyday life is today at the forefront of applied and social sciences. The need to understand, quantify and forecast how individuals and/or populations behave with respect to their surroundings has never been greater, in particular in the face of growing environmental challenges.

The process of decision making at the individual level has been studied extensively in operations research and management sciences, optimization, game theory, economics etc. The traditional approach is concerned primarily with the study of appropriately defined static (equilibrium) states and their properties, assuming that individuals make rational decisions. For constantly evolving systems however, this is an important, yet not sufficient, approach to describe societal behavior. This is a particularly important question if one studies innovation (new products) and science (new information about a product e.g. health benefits) driven problems, their complex relationship with policy making, and the ever changing population composition. In such a setting, the factors influencing individual and/or population attitudes are evolving, so the static theory cannot apply.

My research in this area is centered around several dynamic modelling approaches to population behaviour incorporating both objective and subjective decision factors. In this talk I concentrate on two time-dependent extensions of a standard, static model of consumer choice for differentiated products. We use both an agent-based and a PDE computational approach, and we incorporate social network effects. In this setting, an individual's choice depends not only on its characteristics (personality traits, perceived health benefits of a product, price of product, personal income), but also on the consumption choices of others in its social network. Of central interest is how consumers react to the introduction of a new product in the market. We are able to simulate socio-economic decision making criteria, under time-dependent individual and product characteristics, and to compute the adoption level of the new product in the population.

Time and location change: 3PM in South Hall4607.

February 22nd

Title: Calculating target Cataract Surgical Rates for Africa

Speaker: Talithia Williams, Harvey Mudd

Cataract remains the leading cause of blindness in Africa and planning for its treatment is a priority of the World Health Organization's VISION 2020 initiative. The cataract surgical rate (CSR), the number of operations done per million population, is a convenient indicator for planning and monitoring. However, estimating what the CSR needs to be to eliminate blindness requires one to take into account a number of factors and assumptions.

The recently developed Rapid Assessment of Avoidable Blindness (RAAB) survey uses a population-proportional-to-size sampling technique to select a representative group of people over 50 years old to receive a standard eye exam. We use current data from RAAB surveys in Africa to model the epidemiology of visually significant cataract and to estimate the incidence of cataract causing loss of visual acuity at different age levels. In this talk, I describe our method of estimating incidence from prevalence and how this information can be used to help set target CSR's for various geographical locations in Africa, taking into account important differences among populations.

In accordance with the theme of the Hypation Seminar, this talk will conclude with a discussion of the importance of mentoring women and underrepresented minorities in the mathematical sciences. I will share personal experiences and ways that individuals can aid in strengthening the ability of women and minority students to successfully complete graduate programs in the mathematical sciences.

March 1st

Title: From Bernstein-Gelfand-Ponomarev reflections to categorification of cluster algebras

Speaker: Idun Reiten, Norwegian University of Science and Technology

Around 1970 Bernstein-Gelfand-Ponomarev introduced reflection functors between representations of quivers with the same underlying graphs, but with different orientations. They used these functors to give a new interesting proof of Gabriel's classification theorem of the quivers of finite representation type in terms of Dynkin diagrams. We discuss the influence of this work on the recent theory of cluster categories, which were introduced in order to categorify a class of the cluster algebras introduced by Fomin-Zelevinsky. We also talk about some further developments.

This week we will be combining the Hypatian and Algebra Seminars, and calling the whole thing a "Special Colloquium" that will go from 3:30-5:00 with a 10 minute break for refreshments at 3:50PM. Prior to the break, the talk will be introductory, and afterwards it will be at the level of a typical Algebra Seminar.

March 8th

Title: Setting Inventory Levels for Critical Items with Unpredictable Demands

Speaker: Carol Fan, Rand Corporation

Inventory levels help warehouse managers determine when to order replenishments and what amount to order. Setting inventory levels for items with demands that can be predicted by a parametric equation, e.g., standard probability distribution, is relatively simple, but what can one do when demands are "unpredictable," meaning the cannot be modeled by a parametric equation? We look at the problem of setting inventory levels for items that are difficult to predict yet critical.

Talk is via sykpe.

## Fall 2009 Schedule

September 28th

Organizational Meeting

The Hypatian Seminar organizational meeting will be held at 3:30 in South Hall 6635. We will be discussing ideas for the fall and winter quarters. Everyone is welcome--bring ideas!

Agenda:

1. Current amount of money available
2. NSF Grant progess Report
3. Filling in remaining slots in the Seminar
4. Outreach -- possible workshop with Girls Inc

October 5th

Panel Discussion

Topic: How to get a job/post-doc

Confirmed panelists: Emille Davie, Ilsenami Adeboye, Elizabeth Thoren. Bring questions!

October 12th

Title: High Distance Heegaard Splittings

Speaker: Marion Moore, UC Davis

Any 3-dimensional manifold can be decomposed into two simple pieces: a Heegaard splitting. A Heegaard splitting can be regarded as a pair of subcomplexes in the complex of curves of the Heegaard surface. It is possible to relate geometric and combinatorial properties of these subcomplexes with topological properties of the manifold and/or the associated splitting. One such property is the Hemple distance of a Heegaard splitting. I will define the Hemple distance and give examples of desirable characteristics of high distance splittings.

October 19th

Title: Combinatorial Geodesics in Simplicial Complexes

Speaker: Rena Levitt, Pomona

In his 1912 paper, Max Dehn posed three seminal problems in combinatorial group theory: the word problem, the conjugacy problem, and the isomorphism problem. While stated in terms of finitely presented groups, each problem arose naturally in Dehn's study of fundamental groups of $2$-dimensional surfaces. In this talk, I will discuss one method to solve the word problem by constructing a geometric space the group acts on, the Cayley Graph. Then I will discuss using metric conditions to show that groups acting on CAT(0) simplicial complexes are biautomatic, a condition that gives a positive solution to both the word problem and the conjugacy problem for these groups. This relies on looking at the structure of combinatorial geodesics in the spaces.

October 26th

Title: Achievable pebbling numbers

Speaker: Cindy Wyels, CSUCI

Graph pebbling arose in a search for a "natural" proof of a number-theoretic conjecture of Erdös and Lemke, and has since taken on a life of its own. Begin with a distribution of pebbles on the vertices of a graph G. A pebbling move consists of taking two pebbles from a vertex and moving one to any adjacent vertex (while discarding the second). We say the distribution is solvable if at least one pebble may be placed on any target vertex, via a sequence of pebbling moves (possibly of length 0). The pebbling number of G is the smallest integer for which every distribution with that many pebbles is solvable. The pebbling number of a graph of order n must lie between n and 2n-1. We ask which integers may be realized as the pebbling number of a graph of order n. We specify sufficient conditions for an integer to be realized as a pebbling number, identify where certain gaps among potential pebbling numbers must occur, and obtain improved upper bounds for pebbling numbers.

November 2nd

Title: Higher-Dimensional Algebra: Weakening the notion of Equality

Speaker: Alissa Crans, LMU

A fundamental problem in mathematics consists of determining whether two given mathematical structures are 'the same'. For example, knot theorists are interested in knowing when knots are the same, while algebraists like to know when groups are the same. But what exactly do mathematicians mean when they say that two gadgets are the same? Often, they mean "sufficiently the same for our purposes", and that purpose naturally differs from field to field. Higher-dimensional algebra, which enables us to refine our notion of 'sameness', is the study of generalizations of algebraic concepts obtained b y developing category-theoretic analogs of set-theoretic concepts. We will see how higher-dimensional algebra can be used to explore mathematical interpretations of being 'the same' by carefully examining the concept of equality and comparing it to weaker notions of sameness.

November 9th

Titles: Manifolds with Nonnegative Ricci curvature

Speaker: Cynthia Flores

I will present some interactions among the various concepts of curvature and the relatively new concept of isotropic curvature. I will show some of the known results about Betti numbers pertaining to certain compact manifolds of nonnegative isotropic curvature and generalize them for nonnegative isotropic Ricci curvature. The results are proved using the Weitzenbock Formula and Hodge Theory. (Cynthia)

Factors Related to the Success of CSU Chico Students

Speaker: Arielle Leitner

What is a better indicator of student success: High School GPA or SAT score? In this presentation, we will discuss the relation of High School GPA, SAT score, race, gender, parental education and other factors to student success; where success is measured in terms of graduating GPA and years to degree. (Arielle)

November 16th

Title: The Spectrum and Stability for PDEs

Speaker: Elizabeth Thoren, UCSB

The spectrum of a linear operator is a generalization of eigenvalues for a matrix. Just as with eigenvalues and their eigenvectors, the spectrum of an operator tells us how the operator stretches certain vectors. I'll start the talk with a gentle introduction to spectral theory for linear operators and then use spectral theory to define a good notion of linear stability for PDEs. This talk is for a general mathematical audience -- no familiarity with PDEs or functional analysis required.

November 23rd

Title: Morse Theory on Surfaces

Speaker: Mike Williams, UCSB

Morse theory deals with the analysis of critical points of differentiable functions, as in the second derivative test from calculus. Some nice topological interpretations result from this theory. In this talk, I will give an introduction to Morse theory and a discussion of how this theory can be used to distinguish surfaces. Any student with knowledge of multivariable-calculus and linear algebra should be able to understand most of the talk.

November 30th

Title: Agent-based modeling of complex systems, and how to claim your mathematical territory after your doctorate

Speaker: Alethea Barbaro, UCLA

At UCSB, I modeled the spawning route of the Icelandic capelin using an off-lattice interacting particle model. Now as a postdoc at UCLA, I am expected to make an impact well beyond my doctoral work. As such, I have had to explore and claim new mathematical territory. In this talk, I would like to show you how a researcher might expand on her mathematics after her dissertation. I will use my own experiences and my own research as a case study. The aim is that you will walk away from this talk with a basic understanding of the mathematics involved in agent-based complex systems and a more complete idea of how one moves forward as a research mathematician.

## Spring 2009 Schedule

March 30th

Organizational Meeting

The Hypatian Seminar organizational meeting will be held at 3:30 in South Hall 6635. We will be discussing ideas for the fall and winter quarters. Everyone is welcome--bring ideas!

April 6th

Title: Understanding the effects of near-surface geology to earthquake motion via seismogram inversion

Speaker: Dominic Assimaki, Georgia Tech

Observations of seismic ground motion in the last decade have contributed towards the understanding of the effects of near-surface geologic formations to earthquake motion, and have allowed advancements to be made in the state-of-knowledge and modeling of sediment response in-situ. To that end, we present a seismic waveform inversion algorithm that allows estimation of the soil properties and response to earthquake shaking using downhole seismogram array recordings. The algorithm is based on a global optimization scheme complemented by a local least-square fit operator in series, which improves the computational efficiency of the former, while avoiding the pitfalls of using the latter for the optimization of multi-modal, discontinuous and non-differentiable functions. Also, the non-stationary seismic signal is decomposed in the wavelet domain, which allows for equal weighting of the information across all frequency bands. The algorithm is next employed for the estimation of dynamic soil properties at geotechnical arrays operated by a variety of agencies and organizations (SCEC, USGS, CSMIP, Caltrans) in the Los Angeles basin. We show that while the optimization scheme provides robust estimates of the stiffness profiles, the attenuation structures are strongly affected by scattering effects of seismic waves in the near-surface soil layers. We finally present a sensitivity analysis on the dependence of the inverted attenuation structure to the frequency content of seismic input data, and conclude that for strongly heterogeneous soil formations, inversion schemes should explicitly uncouple the material (energy absorption) and scattering (energy redistribution) attenuation mechanisms to properly approximate the physics of earthquake wave propagation in the near-surface.

April 13th

Discussion: Math and the Media

Led by: Brie Finegold

I will be showing some video clips and articles from the popular media that discuss mathematics. You may even learn how to rescue yourself from the following situation:

Person: "What do you do?" (conversation starter)
You: "Oh, I'm a student." (delaying the inevitable)
Person: "And what are you studying?" (interested look on the face)
You: "Oh, I study mathematics." (big smile)
Math-Hater: "Oh, I hate(d) math." (conversation ends)

April 20th

Title: Using Auslander-Reiten Theory to understand a category of poset representations

Speaker: Audrey Doughty, Florida Atlantic University

In this talk, we'll use a combinatorial algorithm commonly used in Auslander-Reiten theory, as well as some special short exact sequences to pin down isomorphism types of representations of a particular poset, P.

April 27th

Speaker: Audra Kosh

Audra has been working with Vadim Ponomarenko (from San Diego State). For the second half of the seminar we can socialize, and I will bring cookies!

May 4th

Title: An Introduction to Modern Homotopy Theory

Speaker: Dr. Julie Bergner, UC Riverside

We'll look at some of the basic ideas of classical homotopy theory in topology, and then discuss how to translate those ideas into more general settings, often outside of topology.

May 11th

Title: On the maximum exponent of circulant primitive matrices with fixed number of nonzero entries in the generating vector

Speaker: Dr. Maribel Bueno, UCSB

This talk explores an interesting problem in Combinatorial Matrix Theory and its equivalent statements in other areas of mathematics.

A matrix is said to be circulant if every row but the first one is obtained by shifting the previous row cyclically one column to the right. The first row of A is called the generating vector.

A matrix A is said to be primitive if there exists a positive integer k such that A^k is a positive matrix. The minimum such k is called the exponent of A.

An open question is: What is the set of exponents attained by circulant primitive matrices?

In this talk we will present a conjecture to this question and give an answer to the question: What is the maximum exponent attained by circulant primitive matrices whose generating vector has exactly r nonzero entries.

This talk will be accessible to undergraduates.

May 25th

Holiday

## Winter 2009 Schedule

January 5th

Title: Intensity Sensors and the Phase Reconstruction Problem

Speaker: Chung-min Lee, CSU Long Beach

Phase information of a light wave plays an important role in many optical applications, such as image recovering, optical design and surface measurement. However, the phase function of a light wave cannot be measured directly. Many phase reconstruction techniques have been developed, and some common ones will be presented. I then will focus on the method of intensity sensors which utilize the relationship between the intensity and phase functions of a light wave. Some results obtained by applying the Transport of Intensity Equation and the Weighted Least Action Principle will be presented, and a few related problems will be discussed.

January 26th

Title: Modeling and Analysis of Collective Motion in Animal Groups

Speaker: 26th Allison Kolpas, UCSB post-doc and alum

Many organisms move collectively in self-organized groups such as schools of fish, flocks of birds, swarms of locusts, and herds of wildebeest. Groups are capable of exhibiting a variety of different collective motion states. For example, a school of fish may swarm about a food source, travel in a highly polarized group, or form a circular milling pattern to avoid sit-and-wait predators. Although switching is observed in nature, the mechanisms behind it are not well understood. In this talk, I will present two models for collective motion which exhibit bistability, where switching may be robustly achieved through noise or external input. The first model, a biologically motivated individual-based model for group formation, displays stochasticity-induced switching between two metastable states. For this model, I will describe a coarse-grained computational framework for model reduction and analysis. The approach involves identifying a single dynamically meaningful coarse observable whose dynamics are described by an effective Fokker-Planck equation. The analysis leads to the construction of an effective potential which is used to perform bifurcation analysis, relating how behavioral interactions among individuals translate into collective movement patterns. The second model, a continuous-time kinetic model for collective motion with coupled oscillator dynamics, is inspired by the engineering literature for groups of autonomous vehicles. For this model, we consider how to design interaction rules which simultaneously stabilize two collective motion states. Variational methods are used to determine an optimal input to the steering control of an agent to induce switching between states.

February 2nd

Short Talks on Dynamical Systems

Speakers: Brittany Erickson and Melissa Hendrata

Brittany and Melissa will give short and accessible introductions to their research. Brittany studies applications to geophysics with Bjorn Birnir, and Melissa studies applications to microbiology also with Bjorn. They will each talk for about 20 minutes with a few minutes for questions at the end of each talk.

February 9th

Title: Vertical Blow-Ups and Applications to Capillarity

Speaker: Thalia Jeffres

The equation that describes the surface of a liquid standing in a capillary tube or container is a prescribed mean curvature equation which shares many features with minimal surfaces. If the container has a corner, the key to understanding the solution to this equation is a very careful examination of the behavior of the unit normal on approach to the corner through various directions. A colleague, Kirk Lancaster, and I used a blow-up procedure to describe which limiting positions were attained. I will describe the problem and some of the techniques used to solve it. This problem is a variational problem, and I will also describe some general features of variational problems. This talk will be accessible to all graduate students.

February 18th (Wed)

Panel Discussion

Note the special meeting time on Wednesday rather than Monday! We will have a panel to lead a discussion on finding an advisor. Bring questions!

February 23rd

Title: Polyhedral complexes and lattices

Speaker: Anne Thomas, Cornell

The class of polyhedral complexes includes many structures, such as simplicial complexes, cubical complexes, and buildings, which are important in many parts of mathematics. We will introduce several beautiful examples, and describe how they can be used to study lattices in locally compact groups.

March 2nd

Title: Pulling Weeds or Sowing Seeds: Women in Graduate Mathematics

Speaker: Abbe Herzig, CUNY Ablany

Some background info about our speaker: Dr. Herzig's research concerns equity and social justice in mathematics and science education at all levels. She is at the beginning of a 6-year research program concerning women and students of color in the post-graduate mathematical sciences, and is also investigating the low numbers of students of color in undergraduate engineering. She has developed courses and programs to help diverse populations of young people discover the relevance of mathematics and science to their interests and realities. She worked for 12 years as a statistician, much of that time for Consumers Union, the publisher of Consumer Reports magazine. She has consulted for the United Nations, the Yale School of Medicine, Brookhaven National Laboratory, and the Legal Defense Fund of the NAACP.

## Fall 2008 Schedule

September 29th

Film Watching

Title: Julia Robinson and Hilbert's Tenth Problem

We will watch this biographical documentary on the life of mathematician Julia Robinson. Robinson was the first woman elected to the mathematical section of the National Academy of Sciences, and the first woman to become president of the American Mathematical Society. This film tells the story of Robinson's work with Russian mathematicians during the cold war that led to a solution to Hilbert's Tenth Problem. For more information, visit zalafilms.

October 6th

Title: The Fundamental Gap Conjecture

Speaker: Julie Rowlett, UCSB

What is the "fundamental gap?" Why is it sufficiently interesting that Yau and m. van de Berg made a conjecture about it? In this talk, I'll speak about joint work with Z. Lu on the Fundamental Gap Conjecture. This is a problem in spectral geometry, so if you are unfamiliar with spectral geometry, here is your opportunity to learn about it!vI will give some fun and elementary (think multivariable calculus!) examples and explain our new results. The proofs of these results are rooted in a few basic principles, so it should be accessible to all math grad students.

October 13th

Title: Determinants of Laplacians

Speaker: Clara Aldana, University of Bonn

In the talk I will first explain how to define regularized determinants of Laplacians on closed manifolds. Then I will define relative determinants of Laplacians on surfaces with cusps and asymptotically cusps ends. At the end I give some reasons why to study them.

October 20th

Title: The Solar Enigma

Speaker: Pascale Garaud, UC Santa Cruz

The solar interior can be observed using Helioseismology, a method developed in the early 1980s. Measurements of plasma flows deep within the Sun have paved the way towards a better understanding of surface magnetic activity, but have also raised a number of new puzzles, most of which remain to be cracked. I will present new research on the subject of the interior rotation profile, and show how applied mathematics can help understand observations by combining large-scale numerical simulations and analytical toy models.

October 27th

Activity

Theme: Fun Math

In honor of Halloween week, we will be having an informal "fun math" session. Everyone is welcome! We'll provide plenty of problems, but feel free to bring your own to share (nothing that requires graduate-level math, please!).

November 2nd

Title: Groups, Tessellations and the Rediscovery of Escher's Solid

Speaker: Iona Mihalia, Cal Poly Pomona

Some simple plane tessellations can be viewed through algebra lens as generated by groups of transformations acting on the plane. Adding one dimension to the game leads us to the surprising rediscovery of Escher's Solid.

November 10th

Short talks on Topology

Speakers: Teresita Ramirez-Rosas and Brie Finegold

Tere and Brie will give short and accessible introductions to their research. Brie studies Geometric Group Theory with Daryl Cooper, and Tere studies Knot Theory with Ken Millet. They will each talk for about 20 minutes with a few minutes for questions at the end of each talk.

November 17th

Title: Synthetic Curvature

Speaker: Guofang Wei, UCSB

In Riemannian geometry we study the shapes and sizes of manifolds with a Riemannian metric. Curvature is some second derivative of the Reimannian metric which gives a quantitive measure of the shape. What's curvature for metric spaces (ones with no differential structure)? While curvature itself may not be defined, curvature (lower or upper) bounds can be defined using synthetic curvature (curvature without derivative). We will start with the curvature of curves and end with some recent development in synthetic curvature.

November 24th

Panal Discussion

Topic: Surviving Quals

There will be a panel of knowledgeable qual passers/qual writers to answer your questions about the dreaded qualifying exams that we all have to take. Discussion will likely include what you should expect, expectations of the graders, what to study, how to study, etc. Bring questions!

## Spring 2008 Schedule

March 31st

Title: Cores for partitions and the symmetric group

Speaker: Monica Vazirani, UC Davis

You cannot study the symmetric group without stumbling across partitions (or Young diagrams). Cores are special partitions that encode particular algebraic and representation-theoretic information about the symmetric group in characteristic p (for instance, the blocks). Cores also arise in the affine symmetric group, as well as in the affine Lie algebra $\widehat {\mathfrak sl}_n$. We will play with the combinatorics of cores and hint at why their role in all these settings is no mere coincidence.

April 7th

Workshop: Introduction to Mathjobs and finding academic positions online!

Led by: Alethea Barbaro, UCSB

In the Hypatian Seminar, I will lead an interactive introduction on how to use Mathjobs, the website where $\mu$ a.e. academic mathematicians find job listings and apply for jobs. In the seminar, I will be able to access my mathjobs account and show how to navigate the site, both finding listings and actually applying for them. Even if you are very early in your grad school career, you should consider coming--seeing this might take the teeth out of applying for jobs when you get there! Feel free to bring questions about the application process!

April 14th

Title: Gender Differences at the Top of the "Ability" Distribution (or: Using Mathematical Modeling to Show why Larry Summers was Wrong)

Speaker: Cathy Weinberger, UCSB Economics Dept.

Low representation in the extreme upper tail of the mathematics test score distribution is often assumed to explain the small numbers of women in engineering, mathematics, computer science and physical science (EMS) college majors and careers. However, this study finds that fewer than one-third of the college-educated white men in the EMS workforce had SAT-Math scores above the threshold previously presumed in the vocational psychology literature. The lower-scoring male EMS college graduates have more than an empty credential; they enjoy the same earnings advantage, relative to other college graduates with the same scores, as high scoring EMS majors. This study also finds that white women enter EMS fields at no more than half the rate of men with the same mathematics test scores. Both the large gender gap and the low ability threshold for EMS entry are robust to modeling mathematics test scores as a noisy measure of ability.

April 21st

Title: "What do you call an eigensheep?";: Formulaic jokes as knowledge displays among undergraduate math and science students

Speaker: Mary Bucholz and Elena Skapoulli, UCSB Linguistics

For the past two years, we have been carrying out an NSF-sponsored study of social interaction among UCSB undergraduate science majors (including math, physics, and chemistry majors), with the goal of understanding how science-oriented interaction can help promote the retention of students, especially but not exclusively women, in these fields. In this informal talk, we'll present a brief orientation to the project and offer some of our initial findings on one area of our research that has emerged as particularly interesting: the role of science humor in students' displays of scientific knowledge.

Interactional studies of scientific practice have focused extensively on what might be called "the serious side of science", such as the interpretation and representation of data. We argue that another key component of scientific cultural practice is the circulation of science-based humor, which helps scientists (and their students) position themselves as members of a scientific community. We show that science humor, like humor generally, operates in part as a ìshort intelligence testî (Sherzer 1985:219) that simultaneously allows the initiator to display specialized knowledge and demands that recipients offer a corresponding display of understanding. Among undergraduate students, such humor creates the opportunity to display a science-oriented identity by allowing even novices to lay claim to a degree of specialized expertise.

May 5th

No Seminar

Film being presented by the PSTAT department about the life and Mathematics of Wolfgang Doeblin. Read flier at http://www.pstat.ucsb.edu/files/WolfgangDoeblin.pdf

May 12th

Speaker: Erica Flapan

May 26th

Memorial Day

June 2nd

Speaker: Luminita Vese, UCLA

## Winter 2008 Schedule

January 14

Title: Effective Classroom Strategies

Speaker: Sanjai Gupta, Harvey Mudd

When people ask me what it's like to be a teacher, I say it's like acting, but you're allowed to make mistakes. So how does one act in the classroom? In this talk you will experience things I do in the classroom and hear practical advice gathered from my own teaching experiences.

January 28th

Title: A new kind of zeta function: When number theory meets graph theory

Speaker: Audrey Terras, UCSD

The talk is an introduction to zeta functions of graphs by comparison with the zeta functions of number theory such as Riemann's zeta function. Basic properties will be discussed, including: the Ihara formula saying that the zeta function is the reciprocal of a polynomial. I will then explore graph analogues of the Riemann hypothesis, the prime number theorem and connections with expander graphs and quantum chaos. References include my joint papers with Harold Stark in Advances in Mathematics. There is also a book I am writing on my website: http://math.ucsd.edu/~aterras/newbook.pdf

February 4th

Title: Groups and Spines

Speaker: Alexandra Pettet, Stanford

One of the best possible situations to be in when studying a group G is to have a nice topological space on which it acts. "Nice" may mean that the space is contractible and cocompact, with the structure of a simplicial complex and a free G-action. This situation can make it possible, for example, to study presentations or cohomology of G. Usually we have to make do with a G-space which is not quite so nice, but we can often get by almost as well. For example, although we may not start with a space which is cocompact, we may be able to describe a G-invariant deformation retract which is cocompact; this is what we call a spine. I will describe examples for some important groups, namely the outer automorphism group of a free group and the special linear group SL_n(Z). I will also explain a theorem showing that our spine for SL_n(Z) is minimal, in the sense that it contains no smaller invariant retract; this is joint work with Juan Souto.

February 11th

Title: Modeling Earthquakes

Speaker: Brittany Erickson, UCSB

Earthquake prediction has been referred to as the "Holy Grail" of seismology. Although scientists disagree on whether or not we will ever be able to accurately predict when they will occur, we have been able to predict statistical quantities about earthquake strength and geographical distribution. It is interesting to note that many phenomena in geophysics obey scaling laws and exhibit fractal behavior. It took many years before these concepts gained any recognition, but their applicability to earthquake prediction is now widely recognized. The purpose of my talk will be to describe a few different ways in which geophysicists (and mathematicians) model earthquakes. I'll cover examples of scale invariance, complexity, and self-organized criticality in applications to geophysics.

March 3rd

Panel Discussion

Topic: Surviving the Qualifying Exams

It's a rite of passage we all go through. This week's seminar will be discussion on different strategies you can use to successfully tackle your quals. Panelists: Jeff Stopple, Alethea Barbaro, Ryan Blair, Melissa Flora, Rena Levitt, and Peterson Tretheway.

March 10th

Panel Discussion

Topic: Math Research

## Fall 2007 Schedule

October 1

Organizational Meeting

The Hypatian Seminar organizational meeting will be held at 3:30 in South Hall 6635. We will be discussing ideas for the fall and winter quarters. Everyone is welcome--bring ideas! Hope to see you there. There will be snacks!

October 8

Informal Discussion on Life as a Teaching Assistant

Led by: Brie Finegold

This week we will have an informal discussion of teaching and being a teaching assistant. This is an opportunity for both inexperienced and experienced TA's to talk about how the first week of classes went, what our expectations and concerns are for the quarter, and how to become better instructors.

October 22

Film Clip Day

Organized by: Brie Finegold

Today we will be showing clips of mathematics in pop-culture (Remember the show Square One with Math Net? If not, it's because you're too young), and people talking about math/science in American culture (A woman computer scientist reading an essay about her life taken from the anthology "She's Such a Geek!"). I would also like to leave a little time at the end to talk about how we've seen math protrayed in the media, especially with relation to women, and what we like/don't like about it. As always, there will be snacks!

October 29

Organized by: Brie Finegold

This coming Monday, we will be welcoming undergraduates in mathematics, especially women, to attend Hypatian Seminar. We will have an informal meeting where graduate students, post-docs, and faculty can talk to undergrads about what it's like to do research, how it was during their first few years of grad school, and what it's like to be a woman in academia. We hope also that undergrads will come share with us their questions and their impressions and opinions of academic life so far.

November 5

Speaker: Sookyung Joo, UCSB

This talk is an introduction to the mathematical theories of liquid crys- tals. Liquid crystal phases form when a material has a degree of positional or orientational ordering yet stays in a liquid state. We present the static and hydrodynamic theories of liquid crystals and consider the minimizers of the energies and solutions of the governing equations as a way to describe the influence of the temperature or applied fields.

November 19

Title: Lie Groups, Number Theory, Spectral Geometry and Conferences!

Speaker: Julie Rowlett, UCSB

There will be two parts. Part I will be a summary of the interesting mathematics of the 6th International Conference on Lie Theory and Geometry, as well as some discussion of the connections between these 3 areas of mathematics. Part II will be a mini-guide for conferences: how to get invited, what to do when you're there, and what to do afterwards. It will be a very participatory talk, lots of questions welcome, and especially towards the end of the second part, comments will be welcome also.

November 26

Title: Fear, Moderation, and Control

Speaker: Debra Lewis, Univ of Santa Cruz

The goal of control theory is to determine what can be accomplished with limited influence and resources; optimal control seeks strategies that give the most bang for the buck. Pontryagin's Maximum Principle states that optimal solutions are solutions of a Hamiltonian system constructed from the cost function and the evolution equation for the state variables. Exploitation of this Hamiltonian structure, particularly the conservation law, is one of the crucial techniques in the analysis of nonlinear control problems. I'll give some background on optimal control and Hamiltonian systems, briefly discuss a famous control system -- the falling/self-righting cat -- that sparked my interest in the role of psychological costs in biomechanical control systems, and introduce a family of cost function modifications that may be useful in modeling such systems. These models combine a position-dependent cost term and a control-dependent moderation term that enforces a bound on the instantaneous control effort; tuning the moderation parameter adjusts the optimal behavior from "do it ASAP, whatever it takes" to "no big deal... chill out."

December 3

Title: An Introduction to the Braid Group

Speaker: Emille Davie, UCSB

The braid group on n strands was defined in the 1940s by Emile Artin and has since become a widely studied and useful tool in low dimensional topology. We will discus several different definitions of the braid group, as well as discuss some braid group representations. Finally, I will give a glimpse into how one representation was used in my thesis.

## Spring 2007 Schedule

April 19

Planning Lunch

Organized by: Alethea Barbaro, UCSB

We will have an organizational lunch to discuss the following topics:

• Mentoring for incoming students
• Potential speakers for next year
• Conferences graduate students want to attend
• Suggested topics for discussions/workshops
All are welcome to attend! Meet at SH 6432 Q at 12:00p.

April 30

Workshop: Introduction to Research Posters

Led by: Alethea Barbaro and Liana Dawson, UCSB

This week in the Hypatian Seminar, we will have an informal workshop about making conference posters using LaTex. There will be a brief presentation offering tips on poster-making and an opportunity to look at the posters both in .tex format and hard copy. As usual, there will be snacks!

May 14

Panel Discussion

Topic: Injecting enthusiasm into your TA section

Brie Finegold and Ricardo Garza will be leading a panel discussion on teaching methodology Monday at 3:30pm in the Hypatian Seminar. The discussion will center on teaching philosophies and different teaching methods in the classroom. Attendees are encouraged to bring anecdotes from sections and classes. Both success stories and horror stories are welcome! This is an opportunity to share thoughts on teaching and will be pretty informal. All are welcome, as always!

There will be brownies and lemon bars and veggies to snack on!!!!

Link to the web page for the list of ideas on being a teaching assistant

Panelists: Alethea Barbaro, Brie Finegold, Melissa Flora, and Ricardo Garza, UCSB

May 21

Panel Discussion

Topic: Reflections on the Job Search

Liana Dawson, Jared Hersh, and John Levitt will be discussing their experiences on the academic job market this year. They will talk about applications, interviews, and pitfalls you might encounter along the way. This will be an informal discussion and there will be lots of time for you to ask any questions you might have. This is a rare opportunity to hear an honest view of the job market from the perspective of graduate students in the math department. For the last few years, panels of this type have been helpful to students in the past who are thinking about going on the job market after graduate school (particularly the academic job market).

Link to notes from the job search discussion

June 4

Title: Things to do the summer *before* graduation so that your last year is NOT a redbull/coffee-infused-sleep-deprived blur of Latex and job applications

Speaker: Julie Rowlett, UCSB

In this talk, I will present a to-do list of *everything* that you will need to have done by graduation and highlight the things you can do in the summer before graduation to make your last year easier. I will also give some general guidelines, insights and suggestions to help ease your last year of graduate school... At the end of the talk, I will also give some ideas, insights, and suggestions for the post-doctoral years.

Link to the slides from Julie's talk

## Winter 2007 Schedule

January 29

Organizational Meeting

Moderated by: Alethea Barbaro, UCSB

The Hypatian Seminar will have an organizational meeting today at 3:30 in South Hall 6635. We will be discussing ideas of the winter and spring quarters. Everyone is welcome--bring ideas! Hope to see you there.

February 5

Title: Hypatia

Speaker: Jeff Stopple, UCSB

Hypatia (370-415 AD) is considered to be the last mathematician of the ancient world. This talk will be about the times she lived in as well as her work and her legacy.

February 12

Title: Biautomaticity and Triangle-Square Complexes

Speaker: Rena Levitt, UCSB

In this talk I discuss the proof of the following theorem: if $K$ is a compact nonpositively curved triangle-square complex, then its fundamental group is biautomatic. A triangle-square complex is a piecewise Euclidean $2$-complex with each $2$-cell isometric to either an equilateral triangle or square of unit side length. This reproves an generalizes earlier results of Gersten and Short.

February 26

Workshop: An Introduction to Beamer

Led by: Alethea Barbaro, UCSB

Beamer is a free program which you can download off the internet to make slick presentations. It plays nicely with LaTex. This will be an introduction to making presentations in Beamer. We will create a talk together which will show what Beamer can do. Then we will post it here for you to access. Come and bring friends!

Link to the Beamer Talk (PDF file)
Link to all the files needed to create the Beamer talk

March 5

Speaker: Brie Finegold, UCSB

Topic: Cool Math from the Annual AAAS Conference

I will talk about some of the interesting mathematics talks I went to in February. Also, I will say what the AAAS is and why more mathematicians should consider becoming members. Come hear a smattering about "stylometry," detecting fraud using mathematics, what math researchers say you should do to improve math ed., and why Toy Story II looked better than the first one.

March 12

Title: The woman who broke the barrier. Sonya Kovalevsky, Jacobi's theorem and algebraic geometry

Speaker: Bjorn Binir, UCSB

We will discuss the works of the woman who broke the gender barrier in mathematics. She was the first major woman mathematician in modern times and the first one to become a professor in mathematics. Her work was fundamental and classical in PDEs, but less well known is that her work on the Kovalevsky top lead to important developments in integrable systems and algebraic geometry in the latter half of twentieth century. She had many brilliant mathematical insights but perhaps the most enduring one was the sufficiency condition in the classical Jacobi's theorem on integrable systems.

## Fall 2006 Schedule

October 2

Organizational Meeting

Moderated by: Alethea Barbaro, UCSB

This year, the seminar will be every Monday from 3:30-4:30PM as the Student Seminar is no longer in that time slot. Please try to make this time available if you are interested, and come THIS MONDAY for a brainstorming and planning session. There will be snacks :)

October 9

Title: The Card Game Set and Phyllis Chinn

Speaker: Richard Spjut, UCSB

The card game Set was created in 1974 by Marsha Falco - then a population geneticist working in Cambridge. She was using visual aids to study combinations of mutations indicated as culprits for epilepsy in German Shepherds. Replacing large amounts of similar data on file cards with symbols, Marsha recognized certain patterns, which inspired the rules of Set. She copyrighted the game in 1988, and while working at Michigan State University began producing copies on a large scale in 1991. It is now produced by Set Enterprises Inc., of Fountain Hills, AZ. The card game is equivalent to finding triplets of elements of $F^4_3$ that sum to zero, where $F^4_3$ is the direct product of four copies of the finite field of order three. Using this representation of the game (hehe), we will explore some questions such as, "what is the largest possible number of cards that do not contain a 'set'?" This game inspires interest in mathematics. Set is also fun to play. Someone else who finds it entertaining and a useful instruction tool is Phyllis Chinn, who graduated in 1969 from UCSB with a dissertation on Graph Isomorphisms. Dr. Chinn has an Erdos number of 1 from a paper concerning the bandwidth of a graph and its complement. I am not a graph theorist nor algebraist - and you don't have to be either to attend this lecture. I encourage undergraduates to attend.

October 16

Panel Discussion

The Hypatian Seminar this Monday will host a few of the faculty and post-docs who have been hired recently at UCSB. There will be discussion and advice on the process of applying for an academic position, both post-doc and tenure-track. Discussion leaders include Stephen Bigelow, Alex Dugas, Jon McCammond, David Sherman, and Robin Wilson. Bring your questions about the application process (or any advice you might have)!

October 23

Title: Chaos and Seismology: An Introduction

Speaker: Brittany Erickson, UCSB

I will talk about the beauty of chaos in dynamical systems related to weather and to earthquakes. Hopefully after this talk you will know more about routes into chaos and properties of the attractors of chaotic systems with respect to ergodicity, mixing and what makes an attractor strange. I will discuss all these concepts via the research I'm doing in the modeling of rock friction and earthquakes. This will be an introductory sort of talk so I would love for you to attend and ask lots of questions.

October 30

Panel Discussion

Topic: Job Applications

This weeks Hypatian Seminar will be a panel discussion on writing CVs, research statements, and teaching statements. If you are applying for academic jobs this year or are starting to think about the application process, then this discussion is designed for you. Bring your questions and don't be shy!

November 6

Speaker: Ben Benoy

November 13

Title: Links between Topology and the Sciences Responses to "Topologists study maps, right?"

Speaker: Brie Finegold, UCSB

In this talk I will link abstract topological ideas to real-life problems. In particular, I'll describe the use of homotopy groups in understanding defects in liquid crystals, and the use of winding number in coordinating data from many robots. Braided in will be a few mentions differential equations/dynamical systems.

November 20

Title: Rope Length

Speaker: Teresita Ramirez-Rosas, UCSB

I will talk about the ropelength problem which asks to minimize the length of a knotted curve subject to maintaining a largest regular neighborhood around the knot. Using the existence of a special line passing through the knot, we have that the ropelength of any nontrivial knot is at least 15.66. This improves the previously known lower bound of 12. I will try to give an idea of the proof of this fact based on the paper of Elizabeth Denne, Yuanan Diao and John M. Sullivan ("Quadrisecants Give New Lower Bounds for the Ropelength of a Knot").

November 27

Conference Reports

Presented by: Liana Dawson and Allison Kolpas, UCSB

We will be discussing job and post-doc information we learned at conferences we attended this quarter. Allison Kolpas will be talking about the "Negotiating the Ideal Faculty Position Workshop" at Rice University. Liana Dawson will be discussing the "STEM Institute for Postdoctorate Preparation" sponsored by Howard University and the University of Texas, El Paso and the Society for Advancement of Chicanos and Native Americans in Science National Conference.

December 4

Discussion of Annual Surveys

Moderated by: Alethea Barbaro, UCSB

We will discuss the 2005 Annual Survey in December's Notices. We will also have old Annual Surveys which we can use for comparison.

## Spring 2006 Schedule

April 21

2005 Annual Survey of Mathematics

Moderated by: Alethea Barbaro and Rena Levitt, UCSB

This Friday we will meet for lunch and discuss the recent Annual Survey which appeared in the February 2006 issue of Notices.

May 5

Speakers : Kelly Delp, Cal Poly SLO and Amber Rosin, Cal Poly Pomona

Alumnae Kelly Delp and Amber Rosin will tell us about their experiences since grad school and answer questions. It will be in a discussion format. This is a good opportunity for graduate students to come and hear what UCSB graduates have done since graduation and ask for advice from people who have searching for and found jobs in academia recently.

May 19

Title: An Introduction to a Discrete Model of Fish Schooling and its Associated System of ODEs

Speaker: Alethea Barbaro

In my research with Bjorn, I am trying to model the schooling behavior of fish. This research is motivated by a desire to track the annual migration of the capelin from the north of Iceland to their feeding ground far north near Jan Mayen and then back and around to the spawning ground south of Iceland. We began our simulations using an existing discrete system which describes the motion of schools of fish. Recently, Bjorn Birnir derived a system of ODEs from this model, which allows us to study a continuous version of the discrete model. In this talk, we will derive this continuous system and discuss how this will help us to predict the behavior of our discrete model by analyzing the associated system of ODEs

Title: Introduction to the KdV Equation

Speaker: Liana Dawson

I will talk briefly about dispersive equations and the history of the Korteweg-de Vries (KdV) equation. Then we will derive a traveling wave solution for the KdV equation. (Liana)

June 2

Discussion on the Two-Body Problem

Featured Speakers: Mary Bucholtz and Jon McCammond, UCSB

Mary Bucholtz and Jon McCammond will talk about the two body problem this Friday from 1-2pm in the Hypatian Seminar. We meet in room 6617. It will be a discussion format.

## Winter 2006 Schedule

February 3

Workshop on Giving Presentations

Led by: Rena Hull, UCSB

We will discuss using Latex and programs such as Xfig and Powerpoint to create presentations.

February 17

Discussion on Teaching Methods

Led by: Alethea Barbaro, UCSB

We will eat lunch together (in 4607) and have an informal discussion about teaching and other topics.

March 10

Title: Collective Motion in Organisms: Modeling and Computations

Speaker: Allison Kolpas, UCSB

Fish, birds, honeybees, as well as many other animal groups, display collective behaviors such as schooling, flocking, and swarming. Behavioral rules can be established experimentally and so individual based models are used frequently when modeling aggregation in animal groups. We study a one-dimensional model of aggregation behavior which exhibits two stable collective states and explore the collective dynamics with both modeling and computation.

## Fall 2005 Schedule

October 14

Title: Hypatia

Speaker: Brie Finegold, UCSB

I'll talk about Hypatia, one of the first female Greek Mathematicians (after whom we've named our seminar). We'll do a math problem from one of the works she edited. And you'll learn of her gruesome death. Plus, there will be some refreshments!

October 28th

Discussion: Fostering Diversity in Graduate School

Led by: Alethea Barbaro and Rena Hull, UCSB

This weeks discussion will focus on encouraging women and minorities to both attend and finish graduate programs.

November 18th

Title: The Life and Work of Mary Ellen Rudin

Speaker: Rena Hull, UCSB

Mary Ellen Rudin is a professor emeritus at the University of Wisconsin, Madison. She is best known for her contributions to the field of set-theoretic topology. I will give a short biography of her life and present one of her famous counterexamples, a normal Hausdorff space whose cartesian product with the interval is not normal.

December 1st

Title: Conservation Laws and Noether's Theorem

Speaker: Helena McGahagan, UCSB

I will outline the life and some of the work of Emmy Noether, a German mathematician who was a professor at Gottingen and later at Bryn Mawr and Princeton. Although perhaps better known for her later work in ring theory, Noether most important accomplishment in physics is a theoretical result relating symmetries to conservation principles. Taking the examples of the wave equation and the Schrodinger equation, I will state some of the conservation laws, such as conservation of energy and momentum that must hold for these equations. Then I will demonstrate how Noether's theorem generates these laws from the symmetries of the equation.