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; Canceled because of snowstorm
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:
March 16th A 2-Handle Formula for Skein Lasagna Modules with 1-Dimensional Inputs
Imogen Montague, UT Austin
Abstract: Last year, Ren–Sullivan–Wedrich–Willis–Zhang introduced a modified skein lasagna package of invariants for 4-manifolds called skein lasagna modules with 1-dimensional inputs. By leveraging Rozansky–Willis invariants of links in connected sums of S^1xS^2s, this resulting theory was conjectured to be more amenable for computations of the invariants for 4-manifolds built out of both 1- and 2-handles. We show that this is indeed the case by expressing the skein lasagna module with 1-dimensional inputs of such a 4-manifold in terms of a certain quotient of the cabled gl_2-Rozansky–Willis homology of the attaching link, analogous to Manolescu–Neithalath’s 2-handlebody formula. The extra quotienting step arises due to the appearance of a new relation called the lasso relation, which does not appear in the context of ordinary skein lasagna modules. This is joint work with Ian Sullivan.
March 9th: 4-dimensional skein modules and handle attachments
Gage Martin, Harvard University
Abstract: 4-dimensional skein modules are a recent tool developed for the study of 4-manifolds. Applications of these skein modules sometimes rely on an understanding standing of how these change under handle attachments. In this talk we will review an introduction to these modules as well as stating and proving general formula for how these modules change under 1-, 2-, and 3-handle attachments. These generalize existing formula of Chen, Manolescu-Neithalath, Manolescu-Walker-Wedrich, and Ren-Willis.These formula are derived from a complete description of the gluing homomorphism on skein modules. This description was also introduced independently by Blackwell-Krushkal-Luo. This is joint work with Mary Stelow and Mira Wattal.
March 2nd: Constraints on Lefschetz fibrations with 4-dimensional fibers
Juan Muñoz-Echániz, Stony Brook;
Abstract: I will describe a new constraint on the topology of smooth Lefschetz fibrations with 4-dimensional fibers, arising from Seiberg--Witten theory. I will explain how it yields smooth isotopy obstructions for products of Dehn twists on self-intersection -2 spheres in 4-manifolds. As an application, we give a negative answer to a question of Donaldson asking whether, for a closed simply-connected symplectic 4-manifold, the symplectic Torelli group is generated by squared Dehn twists on Lagrangian spheres. Based on joint work with H. Konno, J. Lin, and A. Mukherjee.
February 23rd: Currents are dual to curves Canceled because of snowstorm
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.