In 1983 Jeanne Duflot published some results showing that certain long exact sequences were, in fact, short exact. Her methods confined her to smooth actions. Recently, Matthias Franz, Volker Puppe and I have needed to reconsider Duflot's results, and, in the process, we arrived at new proofs that also work for continuous actions on topological manifolds. The main tool in the proof is a spectral sequence that is an equivariant version of Poincare - Alexander - Lefschetz duality. The proof also makes use of some basic properties of Cohen - Macaulay modules and a little bit of local cohomology.

I will discuss about quantifiers, why one may want to eliminate them and about a joint result with S. Starchenko (University of Notre Dame). This talk should contain very little analysis.

This one hour documentary follows Paul Erdos as he travels the world solving math problems. It features a number of famous mathematicians talking about his influence, and the way that mathematics is done in reality. As usual, pizza follows in the Grad Club.

This talk focuses on Koszul duality of quadratic algebras. We will quickly review the basic definition and important properies of twisted morphism from a (differential graded) coalgebra to a (differential graded) algebra, equivalent characterization of Koszul morphisms, and the adjunction between cobar and bar constructions.Then we apply this to quadratic algebras, and some classical examples will be introduced

In 1988, Delzant showed how to construct a toric manifold from a special type of polytope (now called a Delzant polytope). This result, combined with the Atiyah, Guillemin-Sternberg convexity theorem, establishes a 1-1 correspondence between symplectic toric manifolds and Delzant polytopes. A few years later, Lerman and Tolman did the same with toric orbifolds, thus establishing an analogous correspondence in this more general case, though the polytopes are now more general and come with weights attached to each facet. In this talk, we will focus on a very specific case of the Lerman-Tolman construction; that of constructing a weighted projective space starting with a weighted (non isosceles) triangle.

There is a strong relationship between involutions on compact manifolds and binary codes. Constructions on the side of codes have their counterparts for involutions. Every binary, self-dual code can be obtained from an involution on a 3-dimenional compact manifold with 'maximal' number of isolated fixed points. The code in turn determines the cohomology algebra structure of the manifold. Certain properties of the code are reflected in the geometry of the manifold.

The talk is based on joint work with M. Kreck.

In this talk, we introduce the notion of the essential dimension of an algebraic structure and discuss some recent results on the essential dimension of certain classes of central simple algebras. We also relate these results to the essential dimension of split simple groups of type $A_n$.