Week of February 8, 2026

February 9, 2026
Geometric Analysis and Application Widths, Index, Intersection, and Isospectrality Jared Marx-Kuo - Rice University 3:45pm -
KT 906
Geometry, Symmetry and Physics Stabilization of Kac polynomials along root strings Vladyslav Zveryk - Yale University 4:30pm -
KT801
February 10, 2026
Geometric Analysis Learning Seminar Geometric Analysis Learning Seminar 10:30am -
KT 801
Group Actions, Geometry and Dynamics TBA Max Weinreich - Harvard University 4:30pm -
February 12, 2026
Analysis Support of semiclassical measures in higher dimensions Elena Kim - MIT 4:00pm -
KT 201
Quantum Topology and Field Theory TBA Helen Wong - Claremont McKenna College 4:30pm -
KT 801
February 13, 2026
Learning seminar on Matroids and Algebraic Cycles Learning seminar on Matroids and Algebraic Cycles 2:15pm -
KT 801
Learning seminar on Groups, Geometry and Dynamics Learning seminar on Groups Geometry and Dynamics Ethan Cohen - 4:00pm -
KT 801

Abstracts

Week of February 8, 2026

February 9, 2026
Geometric Analysis and Application Widths, Index, Intersection, and Isospectrality 3:45pm -
KT 906

In this talk, I will discuss a series of works on Gromov’s p-widths, $\{\omega_p\}$, on surfaces. For ambient dimensions larger than $2$, $\omega_p$ morally realizes the area of an embedded minimal surface of index p. This characterization was historically used to prove the existence of infinitely minimal hypersurfaces in closed Riemannian manifolds. In ambient dimension $2$, $\omega_p$ realizes the length of a union of (potentially immersed) geodesics, and heuristically, $p$ is equal to the sum of the indices of the geodesics plus the number of points of self-intersection. Joint with Lorenzo Sarnataro and Douglas Stryker, we prove upper bounds on the index and vertices, making progress towards this heuristic. Along the way, we prove a generic regularity statement for immersed geodesics. If time allows, we will also discuss the isospectral problem for the p-widths and how surfaces provide a convenient setting to investigate this. 
Geometry, Symmetry and Physics Stabilization of Kac polynomials along root strings 4:30pm -
KT801

In this talk, I will present the stabilization phenomenon of cohomology groups and Kac polynomials associated with moduli spaces of quiver representations. Specifically, for Q and chosen dimension vectors d and e satisfying reasonable conditions, the cohomologies of various types of quiver varieties associated with dimension vectors d+ne stabilize as e tends to infinity. I will provide explicit generating functions for these stabilized dimensions and explain the implications for root multiplicities of Kac-Moody Lie algebras.
February 10, 2026
Geometric Analysis Learning Seminar Geometric Analysis Learning Seminar 10:30am -
KT 801

TBA
Group Actions, Geometry and Dynamics TBA 4:30pm -
February 12, 2026
Analysis Support of semiclassical measures in higher dimensions 4:00pm -
KT 201

A central question in quantum chaos is how classical chaotic dynamics influence quantum behavior. On compact Riemannian manifolds, pure quantum states correspond to Laplacian eigenfunctions. The quantum unique ergodicity (QUE) conjecture of Rudnick and Sarnak predicts that on hyperbolic manifolds, all high-energy eigenfunctions become uniformly distributed. The asymptotic behavior of eigenfunctions can be formulated in terms of semiclassical measures, which describe the microlocal distribution of eigenfunction mass. One approach towards the QUE conjecture applies microlocal analysis and uncertainty principles to characterize the support of semiclassical measures. I will discuss recent work that uses the breakthrough higher-dimensional fractal uncertainty principle of Cohen. Using this uncertainty principle, we prove the first result on the support of semiclassical measures on real hyperbolic n-manifolds. To explain some of the main proof ideas, we will discuss work on the toy model of quantum cat maps. This is joint work with Nicholas Miller.
Quantum Topology and Field Theory TBA 4:30pm -
KT 801

TBA
February 13, 2026
Learning seminar on Matroids and Algebraic Cycles Learning seminar on Matroids and Algebraic Cycles 2:15pm -
KT 801

TBA
Learning seminar on Groups, Geometry and Dynamics Learning seminar on Groups Geometry and Dynamics 4:00pm -
KT 801

TBA