Harvard/MIT Algebraic Geometry Seminar
Fall 2018
Tuesdays at 3 pm
The Harvard/MIT Algebraic Geometry Seminar will alternate between MIT
(2142) and Harvard (Science Center 507).
*****We are no longer going by Harvard time. The seminar will start at 3 sharp!*****

Sept 112018
SC 507 Harvard
Jack Huizenga, Penn State
Moduli of sheaves on Hirzebruch surfaces
abstract±
Let X be a Hirzebruch surface. Moduli spaces of semistable sheaves on X with fixed numerical invariants are always irreducible by a theorem of Walter. On the other hand, many other basic properties of sheaves on Hirzebruch surfaces are unknown. I will discuss two different problems on this topic. First, what is the cohomology of a general sheaf on X with fixed numerical invariants? Second, when is the moduli space actually nonempty? The latter question should have an answer reminiscient of the DrezetLe Potier classification of semistable sheaves on the projective plane; in particular, there is a fractallike hypersurface in the space of numerical invariants which bounds the invariants of semistable sheaves. This is joint work with Izzet Coskun.

Sept 182018
2142 MIT
Austin Conner, Texas A&M
New approaches to upper bounds on the complexity of matrix multiplication
abstract±
I will describe two new paths using algebraic geometry and representation theory to prove upper bounds on the exponent of matrix multiplication. The first approach aims to apply the laser method of Strassen to previously unstudied tensors which uniquely share certain geometric properties with the CoppersmithWinograd tensor. The second approach for upper bounds transforms the problem into that of finding a certain sequence of finite groups and associated representations. The first approach is joint work with Fulvio Gesmundo, JM Landsberg, and Emanuele Ventura.

Sept 252018
SC 507 Harvard
Junliang Shen, MIT (We're starting at 3 pm sharp from now on)
Hilbert schemes and the P=W conjecture for parabolic Higgs bundles
abstract±
The P=W conjecture by de CataldoHauselMigliorini establishes a surprising connection between
the topology of the Hitchin system for the moduli of Higgs bundle and the mixed Hodge structure for the
corresponding character variety with respect to Simpson's nonabelian Hodge theorem.
We will present a proof of the P=W conjecture for the moduli spaces of parabolic Higgs bundles (of arbitrary rank)
associated to five affine Dynkin diagrams. Our proof relies on the study of the tautological classes and the perverse
filtration on the Hilbert scheme of points on surfaces. Based on joint work with Zili Zhang.

Oct 22018
2142 MIT
Tom Bachmann, MIT
abstract±

Oct 92018
SC 507 Harvard
Ignacio Barros, Northeastern
Uniruledness of strata of holomorphic differentials in small genus
abstract±
We address the question concerning the birational geometry of the strata of holomorphic and quadratic differentials. We show strata of holomorphic and quadratic differentials to be uniruled in small genus by constructing rational curves via pencils on K3 and del Pezzo surfaces respectively. Of special interest is the case of genus ten where uniruledness is obtained via the study of the Severi variety of nodal curves on K3 surfaces. We also construct projective bundles over rational varieties that dominate the holomorphic strata with length at most g  1, hence showing in addition that these strata are unirational.

Oct 162018
2142 MIT
Dori Bejleri, MIT
abstract±

Oct 232018
SC 507 Harvard
Tim Magee, Instituto de Mathemáticas, UNAM
abstract±
TBA

Oct 2411noon
2449MIT
Harold Blum, Utah (NOTE UNUSUAL TIME/DAY/LOCATION)
abstract±
TBA

Oct 302018
2142 MIT
John Calabrese, Rice
abstract±
TBA

Nov 62018
SC 507 Harvard
Alex Perry, Columbia
abstract±

Nov 132018
2142 MIT
Lynn Chua, UC Berkeley
abstract±
TBA

Nov 202018
SC 507 Harvard
Laure Flapan, Northeastern
abstract±

Nov 272018
2142 MIT
Aaron Bertram, Utah
abstract±
TBA

Dec 42018
SC 507 Harvard
Rob Silversmith, Northeastern
abstract±

Dec 112018
2142 MIT
TBA
abstract±
This seminar is organized by Joe Harris (Harvard), Davesh Maulik (MIT), Brooke Ullery (Harvard), 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.