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DTSTART:20260308T070000
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DTSTART:20251102T060000
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DTSTART;TZID=America/Toronto:20261006T160000
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URL:https://uwaterloo.ca/pure-mathematics/events/analysis-seminar-david-jek
 el-optimal-transport-free-and
SUMMARY:Analysis Seminar | David Jekel | Optimal transport in the free and\
 nquantum settings
CLASS:PUBLIC
DESCRIPTION:DAVID JEKEL (UNIVERSITY OF OTTAWA) \n\n_Optimal transport in th
 e free and quantum settings_ \nWe discuss several noncommutative generaliz
 ations of the classical\nWasserstein distance of two probability measures 
 on R^d\, or more\ngeneral metric spaces\, which measures the minimal L^2 d
 istance of two\nrandom variables with the given distributions. The first m
 otivation\ncomes from free probability theory\, where ideas from optimal t
 ransport\ntheory have been used to show isomorphism of von Neumann algebra
 s and\nappear in functional inequalities with free entropy\, as well as\np
 roviding a general notion of \"perturbing generators\" of a von Neumann\na
 lgebra. The second motivation comes from quantum information theory\,\nwhe
 re optimal transport theory provides a way to assign distances for\nstates
  on a von Neumann algebra. As we will see\, Duvenhage's version\nof quadra
 tic Wasserstein distance relates quite closely to the Biane\nand Voiculesc
 u's free Wasserstein distance. We discuss these distances\nin a common fra
 mework and demonstrate several properties that make the\nnoncommutative se
 tting more challenging\, including non-separability of\nthe Wasserstein sp
 ace\, and a stark difference between the Wasserstein\nand weak-* topologie
 s on certain state spaces. \nMC 5403 \nZoom Link\n[https://uwaterloo.zoom.
 us/j/94186354814?pwd=NGpLM3B4eWNZckd1aTROcmRreW96QT09]
DTSTAMP:20261023T154430Z
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