Abstracts - Fall 2014

Speaker:  Daniel Murfet

Title: New relations among the simple singularities

Abstract: I will present recent work of Nils Carqueville, Ingo Runkel and Ana Ros Camacho which constructs surprising new relations among the ADE singularities and their associated quivers, inspired by an analogy with conformal field theory. These “generalised orbifolding” relations are naturally studied in a bicategorical setting, where the relations between different simple singularities take the form of the equivalences of categories in Beck’s monadicity theorem.

Speaker: Jorge Pereira

Title: Rank two representations of  fundamental groups of quasi-projective manifolds

Abstract: I will discuss a result by Corlette and Simpson concerning the structure of representations of fundamental groups of smooth quasi-projective varieties in SL(2,C) which are quasi-unipotent at infinity.Then I will explain how to extend their result to arbitrary representations in SL(2,C).  This talk will be based on arXiv:1402.1382, a joint work with F. Loray and F. Touzet.

Speaker:  Julianna Tymoczko

Title:  Geometry and combinatorics of Springer fibers

Abstract:  Springer fibers are a family of subvarieties of the flag variety that are the foundation of a classic example of a geometric representation. Springer first described the symmetric group action on the cohomology of Springer fibers that bears his name, though many others followed with very different constructions, including Borho-MacPherson, Lusztig, Garsia-Procesi.

We will describe key features of the geometry, topology, and combinatorics associated with Springer fibers. We will then discuss a conjecture that Springer fibers have the homology of a (specific) union of Schubert varieties. We will describe some geometric and topological context for this conjecture as well as progress towards its proof.

Speaker:  Jie Wang

Title: The primitive cohomology of theta divisors

Abstract: The primitive cohomology of the theta divisor of a principally polarized abelian variety of dimension g is a Hodge structure of level g-3. In this talk, i will present some general facts and questions (eg. the Hodge Conjecture)  about the primitive cohomology and discuss a recent result (joint with E. Izadi) that the primitive cohomology is an irreducible Hodge structure for the theta divisor in a general abelian fivefold.