Abstracts

Week of August 31, 2025

September 2, 2025
Algebraic Geometry Quantizations and their representations, lecture 2 10:25am -
KT 801

I will discuss formal quantizations and their relation to the filtered ones and then the localization procedure for quantizations (sometimes called the microlocalization).
Geometry & Topology Boundary Currents of Hitchin Components 4:30pm -
KT 207

A hyperbolic structure on a surface is described by a representation of the fundamental group into PSL(2,R). Higher rank Teichmüller theory aims to go beyond hyperbolic geometry by studying moduli spaces of representations into bigger Lie groups, most quintessentially SL(n,R). I will discuss a SL(n,R) version of one piece of hyperbolic geometry—Thurston’s compactification of Teichmüller space. Boundary points of Thurston’s compactification are measured laminations: certain analytic objects generalizing simple closed curves. I will discuss a compactification of the SL(n,R) Hitchin component which is constructed in much the same way, and whose boundary points are geodesic currents which generalize closed curves with more intricate restrictions on self-intersection.
September 4, 2025
Algebraic Geometry Quantizations and their representations, lecture 3 10:25am -
KT 801

I will discuss completions of quantizations, the quantum slice theorem and an application to constructing finite W-algebras.
Quantum Topology and Field Theory Lie groups as other Lie groups over noncommutative rings. 4:30pm -
KT 801

Abstract: In recent and upcoming work joint with Anna Wienhard, Zach Greenberg and Merik Niemeyer, we describe a large class of Lie groups as simpler Lie groups “defined over noncommutative rings”, the simplest example expresses the symplectic group SP_2n as as SL_2 over a matrix ring.  We use this description to construct cluster coordinates on moduli spaces of G local systems on surfaces decorated by partial flags of G at the punctures of S. The cluster algebras and varieties which arise this way are noncommutative versions of those coming from Fock and Goncharov cluster coordinates associated to the split Lie group and full flags of this simpler type. I will give an overview of this theory and give an outlook towards some new perspectives on cluster quantization.  

Seminar talk is supported in part by the Mrs. Hepsa Ely Silliman Memorial Fund.
September 5, 2025
Friday Morning Seminar Friday Morning Seminar 10:00am -
KT 801

We have impromptu and (sometimes) scheduled talks, on topics in probability, combinatorics, geometry, and dynamics.

Everyone is welcome!