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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240916T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20240916T153000
URL:https://uwaterloo.ca/pure-mathematics/events/pure-math-department-collo
 quium
SUMMARY:Pure Math Department Colloquium
CLASS:PUBLIC
DESCRIPTION:BRENT NELSON\, MICHIGAN STATE UNIVERSITY\n\nUniqueness of almos
 t periodic states on hyperfinite factors\n\nMurray and von Neumann initiat
 ed the study of \"rings of operators\" in\nthe 1930's. These rings\, now k
 nown as von Neumann algebras\, are unital\n*-algebras of operators acting 
 on a Hilbert space that are closed\nunder the topology of pointwise conver
 gence. Elementary examples\ninclude square complex matrices and essentiall
 y bounded measurable\nfunctions\, but the smallest honest examples come fr
 om infinite tensor\nproducts of matrix algebras. These latter examples are
  factors—they\nhave trivial center—and are hyperfinite—they contain 
 a dense union\nof finite dimensional subalgebras. Highly celebrated work o
 f Alain\nConnes from 1976 and Uffe Haagerup from 1987 showed that these\ni
 nfinite tensor products are in fact the unique hyperfinite factors.\nHaage
 rup eventually provided several proofs of this uniqueness\, and\none from 
 1989 included as a corollary a uniqueness result for\nso-called periodic s
 tates. This result only holds for some infinite\ntensor products of matrix
  algebras and is known to fail for certain\nother examples\, but in recent
  joint work with Mike Hartglass we show\nthat it can be extended to the re
 maining examples when periodicity is\ngeneralized to almost periodicity. I
 n this talk\, I will discuss these\nresults beginning with an introduction
  to von Neumann algebras that\nassumes no prior knowledge of the field.\n\
 nMC 5501
DTSTAMP:20260504T234222Z
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