| Time | Event |
|---|---|
| 9:00 - 9:30 (Sat) | Coffee and Bagels (RLM lobby) |
| 9:30-10:30 | Jim Bryan: Curve counting on Abelian surfaces and threefolds and Jacobi forms |
| 11:00-12:00 | Max Lieblich: Torelli theorems for the derived category |
| 1:45-2:45 | Laura Matusevich: Regular holonomic D-modules, invariants and hypergeometric systems |
| 2:45-3:30 | Poster Session and Coffee |
| 3:30-4:30 | James McKernan: Effective birationality for Fano varieties. |
| 4:45-5:45 | Michael Thaddeus: The universal implosion and the multiplicative horn problem |
| 16:30- | Dinner at Ruby's BBQ |
| 9:30-10:30 (Sun) | John Calabrese: DT invariants of CY3s and birational transformations |
| 10:45-11:45 | Elham Izadi: A uniformization of the moduli space of abelian sixefolds |
| 12:00-1:00 | Aravind Asok: Vector bundles in A^1-homotopy theory |
Jim Bryan: Curve counting on Abelian surfaces and threefolds and Jacobi forms Abstract: We explain how generating functions for curve counting problems on Abelian surfaces and threefolds are given by a certain nice Jacobi form. A new computational technique mixes motivic and toric methods and makes a connection between the topological vertex and Jacobi forms.
Max Lieblich: Torelli theorems for the derived category Abstract: I'll discuss some attempts to prove Torelli-type statements in positive characteristic that replace the Hodge structure with various filtered versions of the derived category. I will review the classical results in this area and then focus on the case of K3 surfaces. This is joint work with Martin Olsson.
Laura Matusevich: Regular holonomic D-modules, invariants and hypergeometric systems Abstract: A fundamental notion in the theory of D-modules is that of regular singularities. The definition, however, is not amenable to algorithmic checking, and is essentially impossible to apply it beyond the simplest examples. Motivated by the question of showing that multivariate hypergeometric systems introduced in the nineteenth century have regular singularities, my collaborators and I developed an invariantizing functor that preserves regularity, as well as other D-module theoretic properties. In my talk, I will explain what regular holonomic D-modules are, and why they are important. Then I will sketch how this property is preserved when taking modules invariants of (suitable) torus equivariant D-modules, and apply this result to answer questions about regularity of hypergeometric differential equations. This is joint work with Christine Berkesch Zamaere and Uli Walther.
John Calabrese: DT invariants of CY3s and birational transformations Abstract: Donaldson-Thomas curve counting invariants are close cousins of Gromov-Witten invariants of Calabi-Yau 3-folds. I will discuss how these behave under birational transformations using Joyce's Hall algebras and derived categories.
Michael Thaddeus: The universal implosion and the multiplicative horn problem Abstract: The multiplicative Horn problem asks what constraints the eigenvalues of two n x n unitary matrices place on the eigenvalues of their product. The solution of this problem, due to Belkale, Kumar, Woodward, and others, expresses these constraints as a convex polyhedron in 3n dimensions and describes the facets of this polyhedron more or less explicitly. I will explain how the vertices of the polyhedron may instead be described in terms of fixed points of a torus action on a symplectic stratified space, constructed as a quotient of the so-called universal group-valued implosion.
Aravind Asok: Vector bundles in A^1-homotopy theory Abstract: I will discuss how the Morel-Voevodsky A^1-homotopy theory has been used to study vector bundles on affine varieties. In particular, I will explain how A^1-homotopy theory can be used to approach classical problems such as ``when does a topological vector bundle on a smooth affine variety admit an algebraic structure?''
Elham Izadi: A uniformization of the moduli space of abelian sixefolds Abstract: For any principally polarized abelian sixefold, we show that 6 times the minimal cohomology class is represented by an algebraic curve by exhibiting a structure of a Prym-Tyurin-Kanev variety of exponent 6 on the abelian variety. This is joint work with Alexeev, Donagi, Farkas and Ortega.
James McKernan: Effective birationality for Fano varieties. Abstract: A projective variety with mild singularities (for example, canonical singularities) is called a Fano variety if -K_X is ample. Fano varieties play a very special role in birational geometry as they are one possible output of the minimal model program and their geometry is simple enough that one can classify them in low dimensions and expect them to be bounded in higher dimensions --- a curve is Fano if and only if it is P^1 and a smooth surface is Fano if and only if it is a del Pezzo surface I describe recent work with Paolo Cascini towards boundedness, as well as some recent exciting independent work of Caucher Birkar.