The MIT G&T Seminar is 3:30-4:30pm every Monday in 2-449, with the exception of MIT holidays.
Spring 2026 Speakers:
February 2nd: Francesco Lin, Columbia;
February 9th: Kristen Hendricks, Rutgers;
February 16th: No Seminar
February 23rd: Dylan Thurston, Boston College;
March 2nd: Juan Muñoz-Echániz, Stony Brook;
March 9th: Gage Martin, Harvard University
March 16th: Imogen Montague, UT Austin;
March 23rd: No Seminar (Spring Break)
March 30th: Louisa Liles, Ohio State University;
April 6th: Surena Hozoori, Brandeis University
April 13th: Ali Daemi, Washington University, St. Louis;
April 20th: No seminar
April 27th: Eugene Gorsky, UC Davis;
May 4th: Ian Zemke, University of Oregon;
May 11th: Saman Esfahani, Harvard University
Titles and Abstracts:
February 23rd: Currents are dual to curves
Dylan Thurston, Boston College
Abstract: The space of geodesic currents on a closed surface is a simultaneous generalization of Teichmüller space, the space of measured laminations, and the space of (not necessarily simple) curves. But they form an infinite-dimensional space that can be hard to get a handle on. We characterize geodesic currents in terms of their intersection number with curves: a functional on curves that satisfies a few simple axioms, most notably a smoothing condition on resolving a crossing, is the intersection number with a (unique) geodesic current, and conversely.
This is joint work with Dídac Martínez-Granado, extending our previous criterion for extending curve functionals to geodesic currents, and has applications to counting problems.
February 9th: Real Heegaard Floer homology and localization
Kristen Hendricks, Rutgers;
Abstract: In the past few years there have been a host of remarkable topological results arising from considering "real" versions of various gauge and Floer-theoretic invariants of three- and four-dimensional manifolds equipped with involutions. Recently Guth and Manolescu defined a real version of Lagrangian Floer theory, and applied it to Ozsváth and Szabó's three-manifold invariant Heegaard Floer homology, producing an invariant called real Heegaard Floer homology associated to a 3-manifold together with an orientation-preserving involution whose fixed set is codimension two (for example a branched double cover). In this talk we use tools from equivariant Lagrangian Floer theory, originally developed by Seidel-Smith and Large in a somewhat different context, to produce a spectral sequence from the ordinary to real Heegaard Floer homologies in their simplest "hat" version, in particular proving the existence of a rank inequality between the theories. Our results apply more generally to the real Lagrangian Floer homology of exact symplectic manifolds with antisymplectic involutions. Along the way we give a little history and context for the appearance of such spectral sequences in Heegaard Floer theory.
February 2nd: Dirac spectral flow and Floer theory of hyperbolic three-manifolds
Francesco Lin, Columbia;
Abstract: In this talk I will address the problem of determining the monopole Floer homology of a hyperbolic three-manifold purely in terms of its geometric invariants (such as volume and lengths of closed geodesics). In particular, I will outline a strategy that under good circumstances allows to determine the Floer homology of a hyperbolic torsion spin^c three-manifold (Y,s) with b_1(Y)=1, and exhibit some concrete instances in which the resulting group is non-trivial. This is joint work with M. Lipnowski.