Time: Some Thursdays at 3:304:30
Place: South Hall 6635
Date  Speaker  Abstract 
9 Oct.  Daryl Cooper  The hyperreals 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 hyperreals have been appearing in many areas of math, in part because they offer conceptual simplification and shorter proofs. See Terence Tao's blog http://terrytao.wordpress.com/2007/06/25/ultrafiltersnonstandardanalysisandepsilonmanagement/ We will construct the hyperreals, 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 hyperreals. 
16 Oct. 


23 Oct.  Paul Atzberger  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 

13 Nov.  Mihai Putinar 

20 Nov. 


4 Dec.  Ken Goodearl 

11 Dec.  Dave Morrison 

8 Jan.  Hector Ceniceros 

15 Jan.  Jeff Stopple 

22 Jan.  Stephen Bigelow 

29 Jan.  Xianzhe Dai 

5 Feb. 


12 Feb.  Jon McCammond 

19 Feb.  Ken Millett 

26 Feb.  Medina Price 

5 Mar. 


12 Mar.  Zhenghan Wang  2vector 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  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 noncommutative fields (also called division algebras), which in this talk will all be finitedimensional vector spaces over commutative fields. The quaternions (fourdimensional 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 

30 Apr.  JeanPierre Fouque 

7 May 


14 May  Lihui Chai 

21 May 


28 May 


4 Jun.  Jordan Schetler  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. 