Published on Department of Mathematics Calendar (https://calendar.math.yale.edu)

Week of February 1, 2026

February 2, 2026
Geometric Analysis and Application [3]	Minimal submanifolds, higher expanders, and waists of locally symmetric spaces	Ben Lowe - University of Chicago	3:45pm - KT 906
Geometry, Symmetry and Physics [4]	Stable homology of moduli spaces, and moments of families of quadratic L-functions over function fields	Dan Petersen - Stockholm and IAS	4:30pm - KT 801

February 5, 2026
Quantum Topology and Field Theory [5]	Skein valued cluster theory and open Gromov-Witten invariants	Mingyuan Hu - Northwestern University	4:00pm - KT 801
Analysis [6]	Asymptotic linear stability of a class of columnar flow	Shuang Miao - Wuhan University	4:00pm - KT 201

February 6, 2026
Learning seminar on Matroids and Algebraic Cycles [7]	Learning seminar on Matroids and Algebraic Cycles		2:15pm - KT 801
Learning seminar on Groups, Geometry and Dynamics [8]	Ergodicity of geodesic flow and the Hopf argument.	Sebastian Hurtado -	4:00pm - KT801 (or KT 217).

Abstracts

Week of February 1, 2026

February 2, 2026
Geometric Analysis and Application [3]	Minimal submanifolds, higher expanders, and waists of locally symmetric spaces	3:45pm - KT 906	There is by now a broad body of work on minimal surfaces in positively curved ambient manifolds. If the ambient manifold has nonpositive curvature, much less is known. I will present some recent results on minimal submanifolds in nonpositively curved locally symmetric spaces, that are motivated by or have parallels to the positive curvature setting. The proofs bring new tools into the picture from representation theory. Another key ingredient is a new monotonicity formula for minimal submanifolds of low codimension in nonpositively curved symmetric spaces. I will then discuss applications to a program initiated by Gromov to prove statements of the following kind: Suppose we are given two manifolds X and Y, where X is “complicated” and Y is lower dimensional. Then any map f: X-> Y must have at least one “complicated” fiber. If time permits, I will also discuss some applications to systolic geometry, global fixed point statements for actions of lattices on contractible CAT(0) simplicial complexes, and/or non-abelian higher expansion and branched cover stability.
Geometry, Symmetry and Physics [4]	Stable homology of moduli spaces, and moments of families of quadratic L-functions over function fields	4:30pm - KT 801	This is a report of joint work with Bergström-Diaconu-Westerland and Miller-Patzt-Randal-Williams. There is a “recipe” due to Conrey-Farmer-Keating-Rubinstein-Snaith which allows for precise predictions for the asymptotics of moments of many different families of L-functions. We consider the family of all L-functions attached to hyperelliptic curves over some fixed finite field. One can relate this problem to understanding the homology of the moduli space of hyperelliptic curves, with symplectic coefficients. With Bergström-Diaconu-Westerland we compute these stable homology groups, together with their structure as Galois representations. With Miller-Patzt-Randal-Williams we prove a uniform range for homological stability. Together, these results imply the CFKRS predictions for all moments in the function field case, for all sufficiently large (but fixed) q.

February 5, 2026
Quantum Topology and Field Theory [5]	Skein valued cluster theory and open Gromov-Witten invariants	4:00pm - KT 801	For a Lagrangian submanifold in a CY3, Ekholm and Shende defined a wavefunction living in the HOMFLY-PT skein module of the Lagrangian, which encodes open Gromov-Witten invariants in all genus. In this talk, we study a skein-valued cluster theory that generalizes quantum cluster theory and allows us to compute these wavefunctions in a range of examples. Our results agree with the physical prediction known as the topological vertex. Along the way we introduce a skein dilogarithm and prove a pentagon relation, generalizing previously known forms of the pentagon identity. This talk is based on joint works with Schrader, Zaslow, and Shende.
Analysis [6]	Asymptotic linear stability of a class of columnar flow	4:00pm - KT 201	Constructing dynamical global-in-time solutions to 3D incompressible Euler equation is in general challenging. Recently Guo-Pausader-Widmayer made a breakthrough in this direction by proving asymptotic stability of a uniform-rotating static solution. Their approach heavily depends on the “uniform-rotating” of the background solution. In this talk I will present some recent progress on asymptotic linear stability of a more general columnar flow with non-uniform rotation. This is a joint work with Siqi Ren (Zhejiang U of Technology) and Zhifei Zhang (Peking U).

February 6, 2026
Learning seminar on Matroids and Algebraic Cycles [7]	Learning seminar on Matroids and Algebraic Cycles	2:15pm - KT 801	TBA
Learning seminar on Groups, Geometry and Dynamics [8]	Ergodicity of geodesic flow and the Hopf argument.	4:00pm - KT801 (or KT 217).	We will discuss the ergodicity of anosov diffeomorphisms and the geodesic flow in negative curvature, talk about pathological foliations and Fubini’s nightmare.

Links
[1] https://calendar.math.yale.edu/list/calendar/grid/week/2026-W05 [2] https://calendar.math.yale.edu/list/calendar/grid/week/2026-W07 [3] https://calendar.math.yale.edu/seminars/geometric-analysis-and-application [4] https://calendar.math.yale.edu/seminars/geometry-symmetry-and-physics [5] https://calendar.math.yale.edu/seminars/quantum-topology-and-field-theory [6] https://calendar.math.yale.edu/seminars/analysis [7] https://calendar.math.yale.edu/seminars/learning-seminar-matroids-and-algebraic-cycles [8] https://calendar.math.yale.edu/seminars/learning-seminar-groups-geometry-and-dynamics [9] https://calendar.math.yale.edu/list/calendar/grid/week/abstract/2026-W05 [10] https://calendar.math.yale.edu/list/calendar/grid/week/abstract/2026-W07