Abstracts

Week of February 22, 2026

February 23, 2026
Geometric Analysis and Application Splitting a manifold with (spectral) Ricci lower bounds 3:45pm -

In this talk, I will discuss the geometry of smooth complete manifolds where the first eigenvalue of the operator −γΔ + Ric, for γ > 0, is bounded from below. Here, Ric denotes the (pointwise) lowest eigenvalue of the Ricci tensor. This condition is weaker than a pointwise lower bound on Ricci curvature. In particular, I will focus on the following result. Let (Mⁿ,g) be a complete non-compact Riemannian manifold with at least two ends, and with n≥2. Assume u is a positive function on M satisfying −γΔu+Ric*u≥0 and γ<4/(n-1). Then, Mⁿ is isometric to the product of IR x Nⁿ⁻¹. This extends a result of Cheeger–Gromoll from 1971, and the bound required on γ is sharp. Joint work with M. Pozzetta and K. Xu.

https://yale.zoom.us/j/91979343134
February 24, 2026
Geometric Analysis Learning Seminar Geometric Analysis Learning Seminar 10:30am -
KT 801

TBA
Geometry, Symmetry and Physics Graded characters of Verma modules via the sphere trace 10:30am -
KT 329

I will talk about twisted traces on quantized Coulomb branches. Any Verma module over a quantized Coulomb branch gives rise to a twisted trace. For conical Coulomb branches there is also a trace introduced by Gaiotto and Okazaki (“sphere trace”). I will show how the sphere trace allows us to compute the graded character of Verma modules in certain cases. Based on joint work in progress with Vasily Krylov.
February 25, 2026
Group Actions and Dynamics Random Walks on the Group of Planar Isometries and Local Limit Theorems 4:00pm -
KT205
We consider the fine-scale behavior of random walks on R^2 generated by successively applying independent random isometries to the origin.
We show that the walk equidistributes at a superpolynomial rate if the rotation parts satisfy a Diophantine condition,  and at a stretched exponential rate if the rotation parts are suitably algebraic. This extends results due to Varju and Lindenstrauss forisometries of R^3 to the more commutative and amenable setting of planar isometries. Based on joint work with Felipe Hernandez.
February 26, 2026
Analysis Critical collapse in 2+1 gravity 4:00pm -
KT 201

Starting with the work of Choptuik ‘92, numerical relativity predicts that naked singularity spacetimes arise on the threshold of non-collapse and black hole formation, a phenomenon referred to as critical collapse. In this talk, I will present for 2+1 gravity the first rigorous construction of threshold naked singularities in general relativity. Joint work with Igor Rodnianski (Princeton University).
Quantum Topology and Field Theory Finite N indices from branes and negative branes 4:30pm -
KT 801

Finite-N effects in large-N gauge theories, such as trace relations, are expected to be holographically dual to non-perturbative phenomena in string theory, such as Giant Graviton branes. A convenient setting to study these effects are supersymmetric indices of U(N) gauge theories. The finite-N indices can be reproduced by a series of corrections to the infinite-N result, known as the Giant Graviton expansion.

In this talk I will present a generalization of the Molien-Weyl formula computing generating functions of invariants of supergroups U(N|M), which arise as gauge groups of brane/negative brane systems in string theory. The formula leads to a new expansion relating finite-N and infinite-N indices of U(N) gauge theories. I will comment on its relation to Murthy’s Giant Graviton expansion and suggest a physical interpretation in terms of branes and negative branes. This talk is based on arXiv:2509.20451 and work in progress with Davide Gaiotto.
February 27, 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 or KT217

We will discuss the dynamics and ergodicity of Anosov diffeomorphisms and related systems.