Description
Thursday [04.04.2019]
16:00-17:00 Szenes
17:30-18:30 Bousseau
Friday [05.04.2019]
10:00-11:00 Némethi
11:30-12:30 Nagy
14:30-15:30 Oberdieck
16:00-17:00 Macri
Saturday [06.04.2019]
10:00-11:00 Bakker
11:30-12:30 Hausel
14:00-15:00 Weyman
Titles and Abstracts
B. Bakker
Title: Global Torelli for symplectic varieties
Abstract: Holomorphic symplectic manifolds are the higher-dimensional analogs of K3 surfaces and their moduli theory enjoys many of the same nice properties. For example, Verbitsky's global Torelli theorem says they are essentially determined by their weight two Hodge structure. In joint work with C. Lehn, we show that many of the results from the smooth case continue to hold for singular symplectic varieties, and we prove a global Torelli theorem. In particular, this gives a new proof in the smooth case which avoids using the existence of a hyperkahler metric and twistor deformations.
P. Bousseau
Title: On the Betti numbers of moduli spaces of semistable sheaves on the projective plane
Abstract: I will describe a new tropical looking algorithm computing Betti numbers (for intersection cohomology) of moduli spaces of semistable sheaves on the projective plane. I will end by some application to some a priori unrelated question in Gromov-Witten theory.
T. Hausel
Title: Very stable Higgs bundles, the nilpotent cone and mirror symmetry
Abstract: I will discuss a conjecture on the existence of very stable Higgs bundles how it implies a precise formula for the multiplicity of the components of the nilpotent cone and its relationship to mirror symmetry. Joint project with Nigel Hitchin.
E. Macri
Title: Derived categories of cubic fourfolds and non-commutative K3 surfaces
Abstract: The derived category of coherent sheaves on a cubic fourfold has a subcategory which can be thought as the derived category of a non-commutative K3 surface. This subcategory was studied recently in the work of Kuznetsov and Addington-Thomas, among others. In this talk, I will present joint work with Bayer, Lahoz, Nuer, Perry, Stellari, on how to construct Bridgeland stability conditions on this subcategory. This proves a conjecture by Huybrechts, and it allows to start developing the moduli theory of semistable objects in these categories, in an analogue way as for the classical Mukai theory for (commutative) K3 surfaces. I will also discuss a few applications of these results.
G. Oberdieck
Title: Gromov-Witten theory of T*E x P1
Abstract: I will explain how to compute the Gromov-Witten theory of the product of the cotangent bundle of an elliptic curve with the projective line, relative to fibers over the P1. The answer is expressed in terms of an operator on Fock space and quasi-Jacobi forms. Joint work with A. Pixton.
A. Szenes
Title: K-theoretic Thom polynomials
Abstract: Thom polynomials of singularities are cohomological obstructions to avoidance of certain type of singularities of maps between varieties. In joint work with Richard Rimanyi, we investigate the K-theoretical versions of these invariants.
J. Weyman
Title: Finite free resolutions and root systems
Abstract: I will summarize the construction of generic rings for finite free resolutions of length 3 over commutative rings and its connection to certain gradings of Kac-Moody Lie algebras corresponding to the graphs T_{pqr}. The interesting feature of this construction is that the generic ring is Noetherian only for resolutions of certain formats for which the graph T_{per} is a Dynkin graph. I will also discuss the consequences of this result for the structure of perfect ideals of codimension three.