Schedule of Graduate Student Colloquium: 2014-15

Time: Some Thursdays at 3:30-4:30

Place: South Hall 6635

Date Speaker
9 Oct. Daryl Cooper
The story of infinitesimals: a conspiracy of silence ?

The hyper-reals are an ordered field containing the real numbers as well as infinitesimals and infinitely large numbers. They have languished for 50 years, spurned by most professionals. The situation recalls the slow acceptance of other extensions of the concept of number. For example, as late as the 1880's, Kronecker disputed the existence of irrational numbers. Recently hyper-reals have been appearing in many areas of math, in part because they offer conceptual simplification and shorter proofs. See Terence Tao's blog We will construct the hyper-reals, and it will become evident that, just from this simple definition, one can deduce most things one wants to know. At the end I might say a few words about doing geometry and topology with the hyper-reals.

16 Oct.

23 Oct. Paul Atzberger
Applied mathematical research at the interface of continuum mechanics and statistical mechanics.

In this informal graduate student seminar we shall discuss mathematical problems in modeling, analysis, and computation that arise in the application areas of soft materials and fluidics. Many recent problems in these fields involve physical regimes where the limits are reached of continuum mechanics descriptions yet taking a fully molecular/atomistic approach would be analytically intractable or computationally expensive. These regimes require the development of new mathematical descriptions, analytic methods, and computational algorithms. We discuss our own work on fluctuating hydrodynamic descriptions for soft materials and fluidics. These methods provide an approach for modelling and simulating elastic microstructures that interact with a fluid when subject to thermal fluctuations. This approach allows for capturing simultaneously such effects as the Brownian motion of spatially extended mechanical structures as well as their hydrodynamic coupling and responses to external flows. We discuss applications of such approaches to problems arising in the rheology of complex fluids, responses of soft materials, and transport within fluidic devices. We also survey the current challenges in this general field concerning mathematical analysis and the development of scalable computation methods.

30 Oct.

6 Nov. Darren Long
A gentle introduction to mapping class groups

13 Nov. Mihai Putinar

20 Nov.

4 Dec. Ken Goodearl
Incidents of Incidence -- Projective Geometry and Synthetic Coordinates.

11 Dec. Dave Morrison

8 Jan. Hector Ceniceros
Magnetic Fluids

15 Jan. Jeff Stopple
Riemann zeros and the heat equation

22 Jan. Stephen Bigelow
Diagrammatic Algebra

29 Jan. Xianzhe Dai
WHy God is a geometer III

5 Feb.

12 Feb. Jon McCammond
From Platonic solids to Lie groups

19 Feb. Ken Millett
Entangled Polymers

26 Feb. Medina Price
2015: Meeting of the Minds

5 Mar.

12 Mar. Zhenghan Wang
>What is a 2-vector space?

2-vector space is a higher version of vector space. I will give a definition and discuss their basic properties. If time permits, some connections to my research.

2 Apr.

9 Apr. Bill Jacob
Non-Commutative Fields”.

In basic undergraduate and graduate algebra courses the subject of (algebraic) fields is introduced, usually culminating in introductory Galois theory. Along side this subject is the study of non-commutative fields (also called division algebras), which in this talk will all be finite-dimensional vector spaces over commutative fields. The quaternions (four-dimensional over the real numbers) are an example you may have bumped into and we will start there. We will then survey some of the highlights of this subject during the 20th century and conclude by posing a few of the open problems that still interest researchers. A course in abstract algebra at the undergraduate level will be ample background for the talk.

16 Apr.

23 Apr. Guofang Wei
Introduction to Comparison Geometry

30 Apr. Jean-Pierre Fouque
From simple random walks to more complex systems

7 May

14 May Lihui Chai
Mathematical tools for seismic imaging

21 May

28 May

4 Jun. Jordan Schetler
Dalibraic Topology

The solution to a topology exercise assigned in my first year of graduate school showed up in a Salvador Dali painting! This talk will review some basic concepts in algebraic topology including cell complexes, the fundamental group, and covering spaces.

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