Wednesday January 30, 2019 4:00 PM  5:30 PM Math Tower P131
 Samuel Grushevsky, Stony Brook University
Cohomology of compactifications of moduli of cubic threefoldsThe 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. CasalainaMartin, K. Hulek, and R. Laza

Wednesday February 06, 2019 4:00 PM  5:30 PM Math Tower P131
 Misha Verbitsky, IMPA/ HSE
Automorphisms of algebraically hyperbolic manifoldsA 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 P131
 Dawei Chen, Boston College / IAS
Volumes and intersection theory on moduli spaces of abelian differentialsComputing volumes of moduli spaces has significance in many fields. For instance, the celebrated Witten’s conjecture regarding intersection numbers on the DeligneMumford moduli space of stable curves has a fascinating connection to the WeilPetersson 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 OkounkovPandharipande also used various ideas in ribbon graphs, GromovWitten theory, and Hurwitz theory. In this talk I will introduce an analogue of Witten’s intersection numbers, defined on the BainbridgeChenGendronGrushevskyMoeller compactification of moduli spaces of Abelian differentials, that can be used to compute the MasurVeech 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 P131
 Junliang Shen, MIT
Perverse filtrations, GopakumarVafa invariants, and hyperkähler geometryFor a hyperkähler variety equipped with a Lagrangian fibration, an increasing filtration is defined on its rational cohomology using the perverse tstructure. We will discuss the role played by this filtration in the study of the topology and geometry of hyperkähler varieties, as well as the connection to curve counting invariants of CalabiYau 3folds. 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 P131
 Benjamin Bakker, University of Georgia
TBA

Wednesday March 06, 2019 4:00 PM  5:30 PM Math Tower P131
 Sophie Morel, Princeton
TBATBA

Wednesday March 13, 2019 4:00 PM  5:30 PM Math Tower P131
 Dan Abramovich, Brown University
Resolving singularities in familiesSemistable reduction is often the first step in constructing
compactified moduli spaces, and can be used to discover their
properties. I will describe workinprogress 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 P131

Spring Break!

Wednesday March 27, 2019 4:00 PM  5:30 PM Math Tower P131

No meeting this week

Wednesday April 03, 2019 4:00 PM  5:30 PM Math Tower P131
 Ignacio Barros, Northeastern University
TBA

Wednesday April 24, 2019 4:00 PM  5:30 PM Math Tower P131
 Valery Alexeev, University of Georgia
TBA

Wednesday May 01, 2019 4:00 PM  5:30 PM Math Tower P131
 Andrew Obus, Baruch College CUNY
TBATBA

