Algebraic geometry seminar

from Monday
January 01, 2018 to Thursday
May 31, 2018
Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars

Wednesday
January 31, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Xuntao Hu, Stony Brook University
Degeneration of abelian differentials and period matrices

The plumbing parameters give local coordinates near the boundary of the Deligne-Mumford 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 P-131
Greg Pearlstein, TAMU
Torelli theorems for special Horikawa surfaces and special cubic 4-folds

We 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 4-folds arising from a cubic 3-fold and a hyperplane intersecting transversely in P^4.


Wednesday
February 14, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Michael Kemeny, Stanford
First steps toward a classification of Betti tables of canonical curves

Whilst 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 P-131
Jian Xiao, Northwestern
Local positivity for curves

One 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 non-ample locus of a big class. (Joint work with N. McCleerey.)


Wednesday
February 28, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Anna Cadoret, Jussieu/Courant
On uniform boundedness of arithmetico-geometric invariants in one-dimensional families

Let $k$ be a finitely generated field of characteristic $p≥ 0$ and $X$ a smooth, separated and geometrically connected curve over $k$. Fix a prime $\ell\not= p$.  I  will describe a general uniform open image theorem for $\ell$-adic representations of the etale fundamental of $X$ due to A. Tamagawa and myself when $p=0$ and E. Ambrosi when $p>0$.  I will explain how this uniform open image theorem can be applied to obtain uniform bounds for arithmetico-geometric invariants encoded in $\ell$-adic cohomology in families of smooth proper  varieties parametrized by $X$. I will discuss more specifically  the $\ell$-primary torsion of abelian varieties (joint with A. Tamagawa) and  of the Galois-fixed part of the geometric Brauer group (joint with F. Charles).


Wednesday
March 07, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Ariyan Javanpeykar, Universitaet Mainz
Arithmetic, algebraic, and analytic hyperbolicity

In the first part of this talk we will discuss different notions of hyperbolicity for algebraic varieties which are conjecturally related by conjectures of Green-Griffiths, 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 P-131
Spring Break!, Stony Brook University
TBA

TBA


Wednesday
March 21, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Cristian Minoccheri, Stony Brook University
1-Cycles on Fano varieties

The geometry of Fano varieties is strongly related to the geometry of low degree rational curves on them. I will discuss one aspect of this relation: for a Fano variety X over \mathbb{C}, the more positive the graded pieces of the Chern character of X are, the simpler the relations among 1-cycles should be. Many examples arise as complete intersections in usual or weighted projective space, where the positivity condition corresponds to the degrees of the defining polynomials being low. In particular, I will discuss new cases of triviality of the first Griffiths group and of the first Chow group being especially simple. (This is joint work with Xuanyu Pan.)


Wednesday
April 04, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Mark Andrea de Cataldo, Stony Brook University
Tutorial on vanishing and nearby cycles, I

The AGS has two empty slots on April 4 (due to a postponement) and April 11 (due to the SBU Gala).

I will fill those slots by giving two informal and introductory lectures, geared to grad students, on how to use nearby and vanishing cycles in algebraic geometry when studying morphisms to a curve.
I will also mention work in progress with D. Maulik on providing evidence towards the P=W conjecture in nonabelian Hodge theory.


Wednesday
April 11, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Mark Andrea de Cataldo, SBU
Tutorial on vanishing and nearby cycles, part II

The AGS has two empty slots on April 4 (due to a postponement) and April 11 (due to the SBU Gala).

I will fill those slots by giving two informal and introductory lectures, geared to grad students, on how to use nearby and vanishing cycles in algebraic geometry when studying morphisms to a curve.
I will also mention work in progress with D. Maulik on providing evidence towards the P=W conjecture in nonabelian Hodge theory.


Wednesday
April 18, 2018

4:00 PM - 5:30 PM
Math Tower P-131
David Hansen, Columbia
What's the deal with rigid analytic spaces?

Rigid analytic spaces are an amazing non-archimedean analogue of complex analytic spaces. Since their invention by Tate in the early 60s, they've developed into a powerful tool in number theory and geometry, with their own richly structured theory. Much of this theory is strongly in parallel with the complex analytic story, but there are many interesting twists. I'll try to survey some of this story, along with some of the successes of this theory and some recent developments. In particular, I'll describe a joint work with Shizhang Li in which we propose an analogue of the Kahler condition in this setting.


Wednesday
April 25, 2018

4:00 PM - 5:30 PM
Math Tower P-131
Kenneth Ascher, Univ. of Washington/MIT
Compactifying the moduli space of degree one del Pezzo surfaces via elliptic fibrations

Stable pairs and KSBA moduli form the generalization of the Deligne-Mumford moduli space of stable curves in higher dimensions. In this talk I will discuss a construction of various modular compactifications of spaces of elliptic surfaces analogous to Hassett's moduli spaces of weighted stable curves. One application of this construction is a stable pairs compactification of the moduli space of degree one del Pezzo surfaces. This is joint work with Dori Bejleri.


Monday
April 30, 2018

4:00 PM - 5:00 PM
Math Tower P-131
Cristian Minoccheri, Stony Brook University
1-cycles and arithmetic of weighted complete intersections

The geometry and arithmetic of Fano varieties are influenced by the geometry of low degree rational curves on them; for 2-Fano varieties (i.e. such that ch_2(X) is positive) this relation is even stronger. While no complete classification of 2-Fano varieties is known, many examples arise as low degree smooth weighted complete intersections, which include cyclic covers of projective space. I will discuss how, for this class of examples, the 2-Fano condition implies that the Chow group of 1-cycles is rather simple. I will also discuss how it implies that weighted complete intersections over function fields of curves satisfy a strong arithmetic property known as weak approximation at all places.


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