Week of February 2, 2025

February 3, 2025
Group Actions and Dynamics Classifying Hyperbolic Ergodic Stationary Measures on K3 Surfaces with Large Automorphism Groups Megan Roda - University of Chicago 4:00pm -
KT 207
Geometry, Symmetry and Physics Curve Counting on Calabi–Yau Quintics Wei-Ping Li - Columbia University 4:30pm -
KT 801
February 4, 2025
Geometry & Topology Connectivity in the space of pointed hyperbolic 3-manifolds Matthew Zevenbergen - Boston College 4:00pm -
KT 207
Applied Mathematics Convergence analysis of classical and quantum dynamics via hypocoercivity Jianfeng Lu - Duke University 4:00pm -
LOM 215
February 5, 2025
Colloquium A strong normal subgroup theorem Tsachik Gelander - Northwestern University 4:00pm -
KT 101
February 6, 2025
Analysis On the Huang-Yang formula for the low-density Fermi gas in 3D Emanuela Giacomelli - LMU Munchen 4:00pm -
Zoom
Quantum Topology and Field Theory Quantum algebras and R-matrices from the equivariant affine grassmannians Wenjun Niu - Perimeter Institute for Theoretical Physics 4:30pm -
Zoom/KT801
February 7, 2025
Friday Morning Seminar TBA 10:00am -
KT 801

Abstracts

Week of February 2, 2025

February 3, 2025
Group Actions and Dynamics Classifying Hyperbolic Ergodic Stationary Measures on K3 Surfaces with Large Automorphism Groups 4:00pm -
KT 207
Let $X$ be a K3 surface. Consider a finitely supported probability measure $\mu$ on Aut(X) such that $\Gamma_{\mu} = \langle Supp(\mu)\rangle < Aut(X)$ is non-elementary. We do not assume that $\Gamma_{\mu}$ contains any parabolic elements. We study and classify hyperbolic ergodic $\mu$-stationary probability measures on $X$.
Geometry, Symmetry and Physics Curve Counting on Calabi–Yau Quintics 4:30pm -
KT 801

I will give a brief review on how to count curves on algebraic manifolds. I will emphasise more on the evolution of counting curves, especially on the importance of change of viewpoints at various stages. I will mention some key new concepts or methods introduced whenever we meet some conceptual or computational difficulties.  Near the end, I will present a method to calculate Gromov–Witten invariants of the Calabi–Yau quintic three-fold.
February 4, 2025
Geometry & Topology Connectivity in the space of pointed hyperbolic 3-manifolds 4:00pm -
KT 207

I will show that the space of pointed infinite volume hyperbolic 3-manifolds is connected but not path connected. This space is equipped with the geometric topology, in which two pointed manifolds are close if they are almost isometric on large neighborhoods of their basepoints. The proof of connectivity will be an application of the density theorem for Kleinian groups. I will then use a combination of results on representations of Kleinian groups and Chabauty spaces of subgroups to construct an infinite family of path components of this space.
Applied Mathematics Convergence analysis of classical and quantum dynamics via hypocoercivity 4:00pm -
LOM 215

In this talk we will review some recent developments in the framework of hypocoervicity to obtain quantitative convergence estimate of classical and quantum dynamics, with focus on underdamped Langevin dynamics for sampling and Lindblad dynamics for open quantum systems. If time permits, we will also discuss some related problems in two-timescale gradient descent and ascent dynamics. 
February 5, 2025
Colloquium A strong normal subgroup theorem 4:00pm -
KT 101
Let \Gamma be an irreducible lattice in a higher-rank semisimple Lie group. We show that every subgroup of infinite index admits a sequence of conjugates that converge to the trivial group (i.e. eventually intersect trivially every finite set). This significantly strengthens the celebrated normal subgroup theorem of Margulis. 
As in classical NST, this result is a consequence of the tension between amenability and property (T) and the proof is more complicated when the ambient Lie group does not have property (T). Most of the works that improved the NST (such as the Stuck–Zimmer theorem and my recent work with M. Fraczyk) assumed property (T). In the recent paper (with Bader and Levit), we established the result in full generality by proving a spectral gap theorem for actions of products of groups, which may replace Kazhdan’s property (T). 
 
Based on a recent joint work with Uri Bader and Arie Levit.
February 6, 2025
Analysis On the Huang-Yang formula for the low-density Fermi gas in 3D 4:00pm -
Zoom

https://yale.zoom.us/j/95303636613

In 1957, Huang and Yang predicted an asymptotic formula for the ground state energy of a dilute Fermi gas in the thermodynamic limit. This formula highlights a remarkable universality, showing that the correlation energy depends solely on the interaction's scattering length. In this talk, I will present a rigorous proof of the Huang-Yang prediction, employing a bosonization approach that interprets suitable pairs of fermions as bosons.
Quantum Topology and Field Theory Quantum algebras and R-matrices from the equivariant affine grassmannians 4:30pm -
Zoom/KT801

In this talk, I will explain my joint work with R. Abedin, in which we construct, for each Lie algebra g, a Hopf algebra and a spectral R-matrix satisfying quantum Yang-Baxter equation. This Hopf algebra is a quantization of the Lie bi-algebra structure on T^*g[t] defined by Yang’s r-matrix, and therefore we call it the Yangian of T^*g. The construction is based on the category of coherent sheaves on the equivariant affine grassmannian associated to the formal group of g, and is motivated by the study of the category of line defects in a 4 dimensional holomorphic-topological field theory. 

Zoom link: https://yale.zoom.us/j/92973039463
February 7, 2025
Friday Morning Seminar TBA 10:00am -
KT 801

A relaxed-pace seminar on impromptu subjects related to the interests of the audience. Everyone is welcome. The subjects are geometry, probability, combinatorics, dynamics, and more!