Abstracts - Spring 2014

Abstracts Spring 2014

Speaker:  Yaim Cooper

Title:  Moduli spaces of stable quotients in genus 0 and 1

Abstract: Stable quotient spaces provide an alternative to stable maps for compactifying spaces of maps. In this talk I will discuss the computation of genus 0 stable quotient invariants of Fano 

and Calabi-Yau complete intersections in P^n, and their relationship to the corresponding Gromov-Witten invariants.  I will also discuss the geometry of moduli spaces of stable quotients which

compactify the space of degree d maps of genus 1 curves to P^n.

Speaker: Angela Gibney

Title: Nonzero-ness of conformal blocks divisors

Abstract:  I'll speak about recent joint work with Prakash Belkale and Swarnava Mukhopadhyay where we study divisor classes on the moduli space of curves using tools from quantum 

cohomology. I will describe some of our results in the context of guiding conjectures about the moduli space of curves. I'll focus on the basic open problem of determining necessary and 

sufficient conditions for these classes to be nonzero, including an answer in the first nontrivial case.

Speaker:  Wei Ho

Title:  Moduli spaces of lattice-polarized K3 surfaces

Abstract:  For moduli spaces of K3 surfaces with a low degree polarization, there are well-known simple GIT constructions. What if one specifies multiple line bundles instead of a single

one? We will discuss representation-theoretic constructions of such spaces, i.e., moduli spaces for K3 surfaces whose Neron-Severi lattices contain specified lattices. These constructions are 

inspired by arithmetic considerations. This is joint work with Manjul Bhargava and Abhinav Kumar.

Speaker: Joseph Ross

Title:  Intersection theory on singular varieties

Abstract: We introduce some ideas from motivic cohomology into the study of singular varieties. Our approach is modeled on the intersection homology of Goresky-MacPherson; our goal is 

to intersect cycles on a stratified singular variety provided the cycles do not meet the strata too badly. We define "perverse" analogues of Chow groups and motivic cohomology. Properties 

include homotopy invariance, a localization theorem, and a splitting theorem. As a consequence we obtain pairings between certain "perverse" cycle groups on a singular variety.