Harvard/MIT Algebraic Geometry Seminar
Fall 2017
Tuesdays at 3 pm
The Harvard/MIT Algebraic Geometry Seminar will alternate between MIT
(4237) and Harvard (Science Center Hall A).

Sep 122017
Hall AHarvard
Rohini Ramadas, Harvard
Dynamics on the moduli space of pointconfigurations on the Riemann Sphere
abstract±
Hurwitz correspondences are a special family of algebraic discrete dynamical systems on the moduli space M_{0,n} parametrizing configurations of n points on P^1. Hurwitz correspondences arise in the study of the topological dynamics of selfmaps of P^1.
Dynamical degrees are numerical invariants associated to algebraic discrete dynamical systems. I will discuss the dynamical degrees of Hurwitz correspondences.

Sep 192017
4237MIT
Giulia Sacca, MIT
Degenerations of hyperkahler manifolds
abstract±
The problem of understanding semistable degenerations of K3 surfaces has been greatly studied and is completely understood (KulikovPinkhamPersson). The aim of this talk is to presentjoint work with J. Kollár, R. Laza, and C. Voisin generalizing some of these results to higher dimensional hyperkähler (HK) manifolds. I will also present some applications, including a generalization of theorem of Huybrechts to possibly singular symplectic varieties and shortcuts to showing that certain HK manifolds are of a given deformation type.

Sep 262017
Hall AHarvard
Alina Marian, Northeastern
On the intersection theory of Hilbert schemes of points on a surface
abstract±
I will describe the structure of natural intersectiontheoretic invariants coming from Chern classes of tautological vector bundles over Hilbert schemes of points on a smooth projective surface. The subject has a long history; I will explain aspects of it, as well as recent contributions in joint work with D. Oprea and R. Pandharipande.

Oct 32017
4237MIT
Yuchen Liu, Yale
Kstability of cubic threefolds
abstract±
We prove the Kmoduli space of cubic threefolds is identical to their GIT moduli. More precisely, the K(semi,poly)stability of cubic threefolds coincide to the corresponding GIT stabilities, which could be explicitly calculated. In particular, this implies that all smooth cubic threefolds admit KählerEinstein metric as well as provides a precise list of singular KE ones. To achieve this, the main new ingredient is an estimate in dimension three of the normalized volumes of kawamata log terminal singularities introduced by Chi Li. This is a joint work with Chenyang Xu.

Oct 102017
SC 411Harvard
ManWai Cheung, Harvard
Quiver representations and theta functions
abstract±
Scattering diagrams theta functions and broken lines were developed in order to describe toric degenerations of CalabiYau varieties and construct mirror pairs. Later, GrossHackingKeelKontsevich unravel the relation of those objects with cluster algebras. In the talk, we will discuss how we can combine the representation theory with these objects. We will also see how the broken lines on scattering diagram give a stratification of quiver Grassmannians using this setting.

Oct 172017
Hall AHarvard
Dave Jensen, U Kentucky
Linear Systems on General Curves of Fixed Gonality
abstract±
The geometry of an algebraic curve is governed by its linear systems. While many curves exhibit bizarre and pathological linear systems, the general curve does not. This is a consequence of the BrillNoether theorem, which says that the space of linear systems of given degree and rank on a general curve has dimension equal to its expected dimension. In this talk, we will discuss a generalization of this theorem to general curves of fixed gonality. To prove this result, we use tropical and combinatorial methods. This is joint work with Dhruv Ranganathan, based on prior work of Nathan Pflueger.

Oct 242017
Hall AHarvard
David Hansen, Columbia
Vanishing theorems in rigid analytic geometry
abstract±
I will review some classical cohomological vanishing theorems due to AndreottiFrankel and Artin, and then explain an analogous result in rigid analytic geometry. I will also explain how I was convinced that excellent rings deserve their name, and why Ofer Gabber is the master of us all.

Oct 312017
4237MIT
Nick Rozenblyum, U Chicago
TBA
abstract±

Nov 72017
4237MIT
Matthew Morrow, CNRS
TBA
abstract±

Nov 142017
Hall A Harvard
Ananth Shankar, MIT
TBA
abstract±

Nov 212017
Hall AHarvard
TBA
TBA
abstract±

Nov 282017
4237MIT
Valentijn Karemaker, U Penn
TBA
abstract±

Dec 52017
4237MIT
Felix Janda, U Michigan
TBA
abstract±

Dec 122017
Hall AHarvard
Marco Gualtieri, U Toronto
TBA
abstract±

Dec 192017
4237MIT
David Smyth, Tufts
TBA
abstract±
This seminar is organized by Joe Harris (Harvard), Philip Engel (Harvard), Brooke Ullery (Harvard), Davesh Maulik (MIT), Georg Oberdieck (MIT), Dhruv Ranganathan (MIT). This seminar is supported in part by
grants from the NSF. Any opinions, findings, and conclusions or
recommendations expressed in this material are those of the author(s)
and do not necessarily reflect the views of the National Science
Foundation.