Y.-P. Lee (Utah)
Functoriality of Gromov--Witten theory under K-equivalent transformations
I will discuss how Gromov-Witten theory behaves under K-equivalent birational transformations. K-equivalence includes flops, crepant resolutions, and in some sense transitions. This is a joint program with H.-W. Lin and C.-L. Wang.

Nick Proudfoot (Oregon)
A taste of symplectic duality
Symplectic duality is a relationship between pairs of algebraic symplectic varieties (or, if you prefer, hyperkahler manifolds). Like mirror symmetry, symplectic duality has a number of different formulations, or phenomena that examples are expected to express. These include

1) cohomological symplectic duality--a duality of vector spaces between certain ordinary and intersection cohomology groups,

2) categorical symplectic duality--Koszul duality between certain categories of sheaves,

3) Goresky-MacPherson duality--a phenomenon relating the spectra of the equivariant cohomology rings of the two varieties.

All of the examples that we understand at present arise from either combinatorics or representation theory. In the combinatorial examples, symplectic duality provides an explanation for certain symmetries of the Tutte polynomial of a matroid. In the representation theoretic examples, it relates to the study of various blocks of Category O.

This is joint work with Tom Braden, Tony Licata, and Ben Webster.

Ionut Ciocan-Fontanine (Minnesota)
Virtual classes via dg-manifolds and virtual Riemann-Roch
I will present a construction of virtual classes, both in K-theory and in Chow groups, for "[0,1] differential-graded manifolds", which are the dg-analogues of varieties with perfect obstruction theory. Further, I will explain certain versions of Riemann-Roch theorems in this context and discuss some applications (cf. also a recent paper by Fantechi and Goettsche). This is joint work with M. Kapranov.