Events for 10/14/2022 from all calendars
LDT Seminar: Jones Polynomial to Volume Conjecture
Time: 1:00PM - 1:50PM
Location: BLOC 302
Speaker: Tushar Pandey, Texas A&M University
Student/Postdoc Working Geometry Seminar
Time: 1:30PM - 2:30PM
Location: BLOC 628
Speaker: JM Landsberg, TAMU
Title: Explicit spaces of constant rank via Steiner bundles
Free Probability and Operators
Time: 4:00PM - 5:00PM
Location: BLOC 306
Speaker: Junchen Zhao, TAMU
Title: Optimal coupling in non-commutative probability
Abstract: In this talk, we would like to introduce optimal coupling of random variables in non-commutative probability spaces, motivated by optimal transport of measure in classical probability theory. We will focus on optimally coupling self-adjoint matrix tuples X = (X_1, ..., X_m) and Y = (Y_1, ..., Y_m) in the probability space (M_n(C), tr). It turns out (even for m > 1 and n = 2,3) they can already demonstrate the complication of non-commutativity and give us interesting examples/intuitions where explicit computations are possible. We will also point out the connections to factorizable maps in operator algebra and quantum information theory; present our new concrete example of matrix tuples in M_3(C) whose optimal coupling requires an embedding into a matrix algebra of larger dimension, namely M_3(C) ⊗ M_3(C); and sketch the proof. At last, we will talk about possible directions of future works and current obstructions. This work was advised by Todd Kemp and David Jekel.