Algebraic geometry seminar

from Tuesday
January 01, 2019 to Friday
May 31, 2019
Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars

Wednesday
January 30, 2019

4:00 PM - 5:30 PM
Math Tower P-131
Samuel Grushevsky, Stony Brook University
Cohomology of compactifications of moduli of cubic threefolds

The moduli space of complex cubic threefolds admits various compactifications, by viewing it as a GIT quotient, a ball quotient, or via the intermediate Jacobians. We compute and compare the (intersection) cohomology of various compactifications. Based on joint work with S. Casalaina-Martin, K. Hulek, and R. Laza


Wednesday
February 06, 2019

4:00 PM - 5:30 PM
Math Tower P-131
Misha Verbitsky, IMPA/ HSE
Automorphisms of algebraically hyperbolic manifolds

A projective manifold M is called "algebraically hyperbolic" if there exists a positive constant A such that the degree of any curve of genus g on M is bounded from above by A(g−1).

It is not hard to see that Kobayashi hyperbolicity implies algebraic hyperbolicity. It is known that Kobayashi hyperbolic manifolds have finite automorphism groups. We have shown that, more generally, algebraically hyperbolic projective manifolds have finite automorphism groups. This is a joint work with Fedor Bogomolov and Ljudmila Kamenova.


Wednesday
February 13, 2019

4:00 PM - 5:30 PM
Math Tower P-131
Dawei Chen, Boston College / IAS
Volumes and intersection theory on moduli spaces of abelian differentials

Computing volumes of moduli spaces has significance in many fields. For instance, the celebrated Witten’s conjecture regarding intersection numbers on the Deligne-Mumford moduli space of stable curves has a fascinating connection to the Weil-Petersson volume, which motivated Mirzakhani to give a proof via Teichmueller theory, hyperbolic geometry, and symplectic geometry. The initial two other proofs of Witten’s conjecture by Kontsevich and by Okounkov-Pandharipande also used various ideas in ribbon graphs, Gromov-Witten theory, and Hurwitz theory. In this talk I will introduce an analogue of Witten’s intersection numbers, defined on the Bainbridge-Chen-Gendron-Grushevsky-Moeller compactification of moduli spaces of Abelian differentials, that can be used to compute the Masur-Veech volumes. This is joint work with Moeller, Sauvaget, and Zagier (arXiv:1901.01785).


Wednesday
February 20, 2019

4:00 PM - 5:30 PM
Math Tower P-131
Junliang Shen, MIT
Perverse filtrations, Gopakumar-Vafa invariants, and hyper-kähler geometry

For a hyper-kähler variety equipped with a Lagrangian fibration, an increasing filtration is defined on its rational cohomology using the perverse t-structure. We will discuss the role played by this filtration in the study of the topology and geometry of hyper-kähler varieties, as well as the connection to curve counting invariants of Calabi-Yau 3-folds. In particular, we will discuss some recent progress on the P=W conjecture for Hitchin systems, and its compact analog for Lagrangian fibrations. Based on joint work with Qizheng Yin and Zili Zhang.


Wednesday
February 27, 2019

4:00 PM - 5:30 PM
Math Tower P-131
Benjamin Bakker, University of Georgia
TBA


Wednesday
March 06, 2019

4:00 PM - 5:30 PM
Math Tower P-131
Sophie Morel, Princeton
TBA

TBA


Wednesday
March 13, 2019

4:00 PM - 5:30 PM
Math Tower P-131
Dan Abramovich, Brown University
Resolving singularities in families

Semistable reduction is often the first step in constructing
compactified moduli spaces, and can be used to discover their
properties. I will describe work-in-progress with Michael Temkin and
Jaroslaw Wlodarczyk in which we prove functorial semistable reduction
for families of varieties in characteristic 0, refining work with Karu
from 2000. Techniques developed for moduli spaces enter in unexpected
ways.


Wednesday
March 20, 2019

4:00 PM - 5:30 PM
Math Tower P-131

Spring Break!


Wednesday
March 27, 2019

4:00 PM - 5:30 PM
Math Tower P-131

No meeting this week


Wednesday
April 03, 2019

4:00 PM - 5:30 PM
Math Tower P-131
Ignacio Barros, Northeastern University
TBA


Wednesday
April 24, 2019

4:00 PM - 5:30 PM
Math Tower P-131
Valery Alexeev, University of Georgia
TBA


Wednesday
May 01, 2019

4:00 PM - 5:30 PM
Math Tower P-131
Andrew Obus, Baruch College CUNY
TBA

TBA


Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars