Yuri Burda (UBC)
What is the simplest dynamics of a polynomial mapping?
To answer the ambiguous question in the title we will look at the behaviour of some polynomials with integer coefficients once reduced modulo a large prime p. The directed graphs whose vertices are residues modulo p and the arrows point from x to f(x) are very similar for the majority of polynomials f of a given degree (and also similar to the corresponding graph for a random mapping). However there are some polynomials for which this graph is especially simple: it splits into a union of several cycles. Schur's conjecture tells that such polynomials are related to another kind of rigid structure: algebraic groups and their automorphisms. We will explore this connection, understand how it was proved for polynomials of one variable and discuss some interesting algebro-geometrical problems one encounters when trying to generalize this picture for endomorphisms of higher dimensional projective spaces.

José González (UBC)
Bivariant Equivariant Cobordism
We define operational versions of algebraic cobordism and equivariant algebraic cobordism. More generally, we associate a bivariant theory to any oriented Borel-Moore homology theory with intersection products. This bivariant theory has the expected features from the case of Chow cohomology. Some of our technical results include Kimura and Gillet type exact sequences for algebraic cobordism and bivariant (equivariant) cobordism. Moreover, when these sequences hold, the equivariant bivariant theory can also be computed as a suitable inverse limit, once again in analogy to the equivariant Chow cohomology case. As an example, we describe the operational equivariant cobordism of arbitrary toric varieties. The results in this talk are joint work with Kalle Karu.

Amnon Neeman (Australian National University)
Hochshcild homology, Grothendieck duality and Brown representability
In a 2008 paper, Avramov and Iyengar studied Cohen-Macauley and Gorenstein morphisms and characterized them in terms of invariants from Hochschield (co)homology. The invariants in question turned out to be related to Grothendieck duality, and in a 2010 paper Avramov, Iyengar, Lipman and Nayak pursued the ideas to prove reduction formulas for the Hochschield (co)homology groups in question. In this talk we will discuss a new approach to the problem, based on Brown representability.