3:45PM: Power structure over the Grothendieck ring of varieties and its applicationsSabir GuseinZadeA power structure over a ring is a method to give sense to an expression of the form $(1 + a_1 t + a_2 t^2 + ...)^m$ where $a_i$ and $m$ belong to the ring so that all the standard properties of the exponential function hold. One has a natural power structure over the Grothendieck ring $K_0(\mathcal{V}_{\mathbb{C}})$ of complex quasiprojective varieties with an interesting geometric description. It can be used both for formulation of some known statements in a short form and for proving new ones. As examples of applications one can give, e.g., an equation for the generating series of classes of Hilbert schemes of zerodimensional subschemes in a smooth complex quasiprojective variety of any dimension, a Macdonaldtype formula for the generating series of generalized higher order orbifold Euler characteristics (with values in the Grothendieck ring $K_0(\mathcal{V}_{\mathbb{C}})$ extended by the rational powers of the complex affine line) of the wreath products of a smooth quasiprojective variety with an action of a finite group.

5:00PM: Betti tables of graph idealsJustin ChenGiven a graph G, one can associate many (often monomial) ideals to it, as invariants of G. This talk will focus on a few specific classes of ideals, which are less wellknown than the standard examples. The commutative algebra of these ideals  in particular, the data of their free resolutions  display fascinating patterns, and have connections to chipfiring, lattice point counting and other combinatorial topics. I will sketch some of these connections for certain classes of graphs; e.g. lowgenus graphs and complete graphs.
