BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:David Jekel (UC San Diego)
DTSTART:20201202T200000Z
DTEND:20201202T210000Z
DTSTAMP:20260420T052850Z
UID:NYC-NCG/33
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/33/"
 >Non-commutative transport of measure</a>\nby David Jekel (UC San Diego) a
 s part of Noncommutative geometry in NYC\n\n\nAbstract\nGiven self-adjoint
  operators $X_1\, \\dots\, X_d$ and $Y_1\, \\dots\, Y_d$\, it is difficult
  to tell when the von Neumann algebra generated by the $X_j$'s and $Y_j$'s
  are isomorphic.  Viewing the operators as non-commutative random variable
 s\, the isomorphism of von Neumann algebras is equivalent to the existence
  of a non-commutative function that will push forward the non-commutative 
 probability distribution of $X = (X_1\,\\dots\,X_d)$ to that of $Y =(Y_1\,
 \\dots\,Y_d)$.  It was proved by Guionnet\, Shlyakhtenko\, and Dabrowski t
 hat certain nice non-commutative probability distributions known as free G
 ibbs laws can be transported to the non-commutative Gaussian distribution\
 , and thus the associated von Neumann algebras are all isomorphic.  More r
 ecently\, we have shown that this transport can be done in a lower triangu
 lar manner\, so that the von Neumann algebra generated by $X_1\, \\dots\, 
 X_k$ is mapped to the von Neumann algebra generated by $Y_1\, \\dots\, Y_k
 $ for $k = 1\, \\dots\, d$.  Furthermore\, this transport arises in a natu
 ral way as the large-$n$ limit of classical transport of measure for rando
 m variables in the space of $d$-tuples $n \\times n$ matrices that approxi
 mate $(X_1\,\\dots\,X_d)$ as $n \\to \\infty$.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/33/
END:VEVENT
END:VCALENDAR