Schedule


Main Lecture Hall


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.


A. Némethi and J. Nagy

Title: The Abel map associated with normal surface singularities I, II

Abstract: The Abel map associated with projective curves is a classical and powerful tool in their studies. We will define its analogue for surface singularities. We list several general properties and we concentrate on the analogue of the Brill-Noether problem, that is, on the determination of the cohomology groups of the line bundles in the Picard group of a resolution. This is a joint work with J. Nagy, his talk will contain several further developments in Part II.


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.