Department of

Mathematics


Seminar Calendar
for events the day of Friday, November 4, 2005.

     .
events for the
events containing  

(Requires a password.)
More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
     October 2005          November 2005          December 2005    
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
                    1          1  2  3  4  5                1  2  3
  2  3  4  5  6  7  8    6  7  8  9 10 11 12    4  5  6  7  8  9 10
  9 10 11 12 13 14 15   13 14 15 16 17 18 19   11 12 13 14 15 16 17
 16 17 18 19 20 21 22   20 21 22 23 24 25 26   18 19 20 21 22 23 24
 23 24 25 26 27 28 29   27 28 29 30            25 26 27 28 29 30 31
 30 31                                                             

Friday, November 4, 2005

3:00 pm in 141 Altgeld Hall,Friday, November 4, 2005

The K-theory of symplectic quotients

Megumi Harada   [email] (University of Toronto)

Abstract: The topology of symplectic quotients is a topic of great interest in many different contexts, including combinatorics, algebraic geometry, representation theory, and gauge theory. We first give an overview and motivation for this subject, and then discuss a surjectivity result which expresses the K-theory of a symplectic quotient M//G in terms of the equivariant K-theory of the original manifold M. This result is the natural K-theoretic analogue of the Kirwan surjectivity theorem for rational cohomology. Along the way, we prove a K-theoretic version of a key lemma of Atiyah and Bott, which states that the equivariant K-theory Euler class of a G-bundle is not a zero divisor, provided that an S^1 subgroup fixes precisely the zero seciton. This lemma is a key result in equivariant symplectic geometry, and (time permitting) we discuss some further applications of this lemma. This is joint work, and work in progress, with Gregory D. Landweber.

4:00 pm in 341 Altgeld Hall,Friday, November 4, 2005

Interpreting Random Graphs in Pseudofinite Fields

Ozlem Beyarslan (University of Illinois at Chicago)

Abstract: A {\bf pseudofinite field} is an infinite field satisfying all first-order properties in the language {0,1,+,x} of rings which hold in {\bf all} finite fields, like having an extension of degree $n$ for every natural number $n>0$. Pseudofinite fields exist and they can be realized for example as ultraproducts of finite fields. An {\bf n-ary random graph} is a set X with a symmetric and irreflexive n-ary relation R (i.e., $R\subseteq X^n$,m such that R is $\Sym(n)$-closed and no two entries of an element of R are equal) such that for any two finite and disjoint subsets A and B of X^{n-1}, there is an $x\in X$ such that R(a,x) and $\neg R(b,x)$ for all $a\in A$ and $b\in B$. In 1974 J.L. Duret interpreted a random binary graph in a pseudofinite field. This has some important model theoretic consequences. We will show that we can interpret a random n-ary graph in pseudofinite fields.