BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Drupal iCal API//EN
X-WR-CALNAME:Events items teaser
X-WR-TIMEZONE:America/Toronto
BEGIN:VTIMEZONE
TZID:America/Toronto
X-LIC-LOCATION:America/Toronto
BEGIN:DAYLIGHT
TZNAME:EDT
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
DTSTART:20230312T070000
END:DAYLIGHT
BEGIN:STANDARD
TZNAME:EST
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
DTSTART:20231105T060000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
UID:69fa3a46e44a4
DTSTART;TZID=America/Toronto:20231121T163000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20231121T173000
URL:https://uwaterloo.ca/pure-mathematics/events/analysis-seminar-170
SUMMARY:Analysis Seminar
CLASS:PUBLIC
DESCRIPTION:IAN CHARLESWORTH\, CARDIFF UNIVERSITY\n\n\"PERMUTATION MATRICES
 \, GRAPH INDEPENDENCE OVER THE DIAGONAL\, AND\nCONSEQUENCES\"\n\nGraph pro
 ducts were first introduced by Green in the context of\ngroups\, giving a 
 mixture of direct and free products. They have\nrecently been studied in t
 he contexts of operator algebras and of\nnon-commutative probability theor
 y by M\\l{}otkowski\, Caspers and Fima\,\nSpeicher and Wysocza\\'nski\, an
 d others. It is interesting to ask how\nproperties of a family of von Neum
 ann algebras are witnessed in a\ngraph product\; while free products and t
 ensor products are well\nunderstood\, their interplay can be quite subtle 
 in this more general\nsetting. With Collins\, I showed how conjugation by 
 random unitary\nmatrices in a tensor product of matrix algebras creates as
 ymptotic\ngraph independence\, when the unitaries are independent and unif
 ormly\ndistributed but only on particular subalgebras. In this talk\, afte
 r\nspending some time introducing the setting\, I will discuss how\ntechni
 ques inspired by the work of Au\, C\\'ebron\, Dahlqvist\, Gabriel\,\nand M
 ale can be used to make a similar statement about random\npermutations lea
 ding to asymptotic graph independence over the\ndiagonal subalgebra\; the 
 combinatorial techniques required involve\nsome interesting subtleties whi
 ch are not apparent at first glance. I\nwill also discuss some consequence
 s for von Neumann algebras. For\nexample\, suppose that $(M_v)_v$ is a col
 lection of finite dimensional\nalgebras. $M_v$ can be embedded into a larg
 er matrix algebra in such a\nway that it is constant on the diagonal\, and
  the standard matrix units\nof $M_v$ are embedded as elements whose entrie
 s are roots of unity.\nThen if $M$ is a graph product of the $M_v$\, we ca
 n find matricial\napproximations of a generating set which enjoy the same 
 properties\,\nand this in turn allows us to show (using techniques of Shly
 akhtenko)\nthat if the if $M$ is diffuse and algebra generated by the $M_v
 $\nwithin $M$ has vanishing first $L^2$ Betti number then $M$ is strongly\
 n1-bounded in the sense of Jung. This is joint work with de Santiago\,\nHa
 yes\, Jekel\, Kunnawalkam Elayavalli\, and Nelson.\n\nThis seminar will be
  held both online and in person:\n\n* Room: MC 5479\n * Zoom link:\nhttps:
 //uwaterloo.zoom.us/j/94186354814?pwd=NGpLM3B4eWNZckd1aTROcmRreW96QT09
DTSTAMP:20260505T184318Z
END:VEVENT
END:VCALENDAR