Wednesday January 31, 2018 4:00 PM  5:30 PM Math Tower P131
 Xuntao Hu, Stony Brook University
Degeneration of abelian differentials and period matricesThe plumbing parameters give local coordinates near the boundary of the DeligneMumford compactification of the moduli spaces of Riemann surfaces. In this talk we introduce a new method to construct smooth abelian differentials on Riemann surfaces near an arbitrary degenerate Riemann surface, in terms of the plumbing parameters. This method further allows us to compute the degeneration of the period matrices, generalizing results of Yamada and Taniguchi.

Wednesday February 07, 2018 4:00 PM  5:30 PM Math Tower P131
 Greg Pearlstein, TAMU
Torelli theorems for special Horikawa surfaces
and special cubic 4foldsWe will discuss recent work with Z. Zhang on Torelli theorems for bidouble covers of a smooth quintic curve and 2 lines in the plane, and cubic 4folds arising from a cubic 3fold and a hyperplane intersecting transversely in P^4.

Wednesday February 14, 2018 4:00 PM  5:30 PM Math Tower P131
 Michael Kemeny, Stanford
First steps toward a classification of Betti tables of canonical curvesWhilst Voisin's resolution of Green's conjecture gives a complete understanding of the shape of the Betti table of a canonical curve, we know very little about the values of the entries of the table. It is natural to hope that these entries contain new geometric information, and maybe even to dream of classifying possible tables in terms of geometry. We will talk about the very first step towards this, which is an analysis of one particular Betti number, namely the "extremal entry", i.e. the last entry on the first row. We will show that this entry records the number of minimal pencils possessed by the curve, counted with multiplicity. One actor in this story is Kleiman's inductive approach to the famous multiple point formula in intersection theory.

Wednesday February 21, 2018 4:00 PM  5:30 PM Math Tower P131
 Jian Xiao, Northwestern
Local positivity for curvesOne of the most important invariants measuring the local positivity of a nef line bundle is the local Seshadri function introduced by Demailly. We first give a brief introduction to this invariant. Then using the duality of positive cones, we show that applying the polar transform from convex analysis to local positivity invariants for divisors gives interesting and new local positivity invariants for curves. These new invariants, studied also independently by M. Fulger, have nice properties similar to those for divisors. In particular, this enables us to obtain a Seshadri type ampleness criterion for movable curves, and give a characterization of the divisorial components of the nonample locus of a big class. (Joint work with N. McCleerey.)

Wednesday February 28, 2018 4:00 PM  5:30 PM Math Tower P131
 Anna Cadoret, Jussieu/Courant
TBATBA

Wednesday March 07, 2018 4:00 PM  5:30 PM Math Tower P131
 Ariyan Javanpeykar, Mainz/Columbia
Arithmetic, algebraic, and analytic hyperbolicityIn the first part of this talk we will discuss different notions of hyperbolicity for algebraic varieties which are conjecturally related by conjectures of
GreenGriffiths, Lang, and Vojta. Then, we introduce an "analytic" notion of hyperbolicity, which interpolates between being Brody hyperbolic and
hyperbolically embedabble. I hope to give a survey of several known results in the first part. In the second part I will focus on arithmetic questions. For instance, Scholl proved that the
moduli of del Pezzo surfaces is arithmetically hyperbolic. In joint work with Daniel Loughran, we investigate the analogous question for Fano threefolds. For instance, we show that the
moduli of Fano threefolds is not arithmetically hyperbolic, by (explicitly) constructing an abelian surface which sits inside this moduli.

Wednesday March 14, 2018 4:00 PM  5:30 PM Math Tower P131
 Spring Break!, Stony Brook University
TBATBA

Wednesday March 21, 2018 4:00 PM  5:30 PM Math Tower P131
 Cristian Minoccheri, Stony Brook University
TBATBA

Wednesday April 11, 2018 4:00 PM  5:30 PM Math Tower P131
 Angela Gibney, Rutgers
TBATBA

Wednesday April 18, 2018 4:00 PM  5:30 PM Math Tower P131
 David Hansen, Columbia
TBATBA

Wednesday April 25, 2018 4:00 PM  5:30 PM Math Tower P131
 Kenneth Ascher, MIT
TBATBA

