Harvard Gauge Theory and Topology Seminar
Harvard Gauge Theory and Topology Seminar
The seminar meets Fridays 3:30-4:30 pm in Science Center 507. The organizers are Peter Kronheimer, Gage Martin, Dylan Galt, William Ballinger, and Clair Xinle Dai. If you'd like to get future announcements, you could send email to xdai@math.harvard.edu.
For those without Harvard IDs, the 5th floor of the Science Center can be accessed by elevator during 3:00-6:00 pm.
Fall 2025
October 24: Yingying Wu (University of Houston）
Title: Singularity models for Z/2 harmonic 1-forms and spinors
Abstract: We introduce local models for a Z/2 harmonic 1-form or spinor on R^{3} and R^{4} near a singular point in their zero loci based on symmetry considerations. The local models are homogeneous with respect to rescaling, with their zero loci given by rays from the origin in R^{3} and cones on the 1‑skeleton of regular 4‑polytopes invariant under subgroups of SO(4).
November 14: Elise LePage (Columbia）
Title: Aganagic’s invariant is Khovanov homology
Abstract: Recently, Aganagic proposed a categorification of quantum link invariants (corresponding to U_q(g) where g is an ADE Lie algebra) using Lagrangian Floer theory in multiplicative Coulomb branches equipped with a potential. Her original proposal was based on insights from string theory, but the resulting definition of categorified link invariants can be made mathematically rigorous. In this talk, I will review her proposal for link invariants and explain my recent proof (joint with Vivek Shende) that Aganagic’s invariant recovers Khovanov homology in the case g=sl(2).
November 21: Isabella Khan (MIT）
Title: Bordered algebras and the wrapped Fukaya category
Abstract: This talk will discuss an isomorphism between endomorphism algebras from the wrapped Fukaya category of a type of punctured surface, and a class of A-infinity algebras related to bordered knot Floer homology. After a brief outline of the constructions and algebraic methods used in the proof, this talk will focus on the model calculations with Fukaya categories that both motivate and help to verify this result.
December 5: Thibault Decoppet (Harvard)
Title: Mixed Verlinde Categories and Invariants of 4-Dimensional 2-Handlebodies
Abstract: I will review how a skein-theoretic construction of Costantino--Geer--Haïoun--Patureau-Mirand produces an invariant of 4-dimensional 2-handlebodies from a finite unimodular ribbon tensor category. I will then discuss more specifically the invariants associated to the mixed Verlinde categories, which are derived from quotients of the Temperley-Lieb category in positive characteristic. This is based on joint work with Benjamin Haïoun.
Spring 2026
Febuary 13: Seraphina Lee (Harvard)
Title: Nielsen realization problem for del Pezzo surfaces
Abstract: The (topological) Nielsen realization problem for a closed, oriented manifold $M$ asks which finite subgroup of $\pi_0(\Homeo^+(M))$ admits a lift to $\Homeo^+(M)$. I will discuss an assortment of results about the Nielsen realization problem for del Pezzo surfaces $M_n := \mathbb{CP}^2 \# n \overline{\mathbb{CP}^2}$, $n \leq 8$, including a classification of finite subgroups $G \leq \pi_0(\Homeo^+(M_2))$ admitting lifts to $\Diff^+(M_2)$ and a comparison of the smooth, complex, and metric versions of the Nielsen realization problem for certain ``irreducible'' finite cyclic subgroups of $\pi_0(\Homeo^+(M_n))$. This talk is based in part on joint work with Tudur Lewis and Sidhanth Raman.
Febuary 27: Shunyu Wan (Georgia Tech)
Title: Surgeries on knots and tight contact structures
Abstract: The existence and nonexistence of tight contact structures on 3-manifolds are interesting and important topics studied over the past thirty years. Etnyre-Honda found the first example of a 3-manifold that does not admit tight contact structures, and later Lisca-Stipsicz extended their result and showed that a Seifert fiber space admits a tight contact structure if and only if it is not smooth (2n-1)-surgery along the T(2,2n+1) torus knot for any positive integer n. Surprisingly, since then no other example of a 3-manifold without tight contact structures has been found. Hence, it is interesting to study if all such manifolds, except those mentioned above, admit a tight contact structure. Towards this goal, I will discuss the joint work with Zhenkun Li and Hugo Zhou about showing any negative surgeries on any knot in S^3 admit a tight contact structure.
March 6: Shuhao Li (Stony Brook)
Title: Topology of Lagrangian submanifolds via open-closed string topology
Abstract: We study Lagrangian submanifolds in standard symplectic vector spaces R^{2n} using ideas from open-closed string topology. Specifically, for a closed, oriented, spin Lagrangian L, we construct a (possibly curved) deformation of the dg associative algebra of chains on the based loop space of L ("open string"), using moduli spaces of pseudo-holomorphic discs with boundaries on L viewed as chains in the free loop space ("closed string"). As an application, we prove that if the second homotopy group of L is zero, then L has non-vanishing Maslov class, generalizing previous results due to Viterbo, Cieliebak-Mohnke, Fukaya and Irie. If time permits, we will speculate on the possible classification of the topology of such Lagrangians in dimension 3.
March 13: Ollie Thakar (Harvard)
April 3: Ciprian Manolescu (Stanford)
April 3: Michael Hutchings (Berkeley)
April 10: William Zhong (SIMIS)
April 17: Qianhe Qin (Stanford)
April 24: Joshua Wang (Princeton)
May 1: Richard Wentworth (Maryland)