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DTSTART:20260308T070000
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DTSTART:20251102T060000
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DTSTART;TZID=America/Toronto:20260819T160000
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URL:https://uwaterloo.ca/pure-mathematics/events/analysis-seminar-ian-charl
 esworth-mixtures-classical-and
SUMMARY:Analysis Seminar | Ian Charlesworth | Mixtures of classical and fre
 e\nindependence
CLASS:PUBLIC
DESCRIPTION:IAN CHARLESWORTH (CARDIFF UNIVERSITY)\n\n_Mixtures of classical
  and free independence_\n\n\\(\\varepsilon\\)-free probability was first i
 ntroduced by Mlotkowski in\nthe early 2000s to understand and model \\(q\
 \)-deformed Gaussian\nvariables\, which interpolate between the usual Gaus
 sian distribution\nat q = 1 and the free semicircular distribution at q = 
 0. It describes\nan independence relation for tuples of algebras\, some in
  free position\nand some in tensor position. A similar construction for gr
 oups (the\ngraph product\, which interpolates between the free product and
  the\ndirect product) was introduced by Green in 1990\, and extended to\no
 perator algebras by Caspers and Fima\, independently recovering\nMlotkowsk
 i's definitions. These objects have attracted quite a bit of\nattention ov
 er recent years\, both from the viewpoint of\nnon-commutative probability 
 theory and in studying their operator\nalgebraic properties directly. I wi
 ll discuss the state of the art\nconcerning \\(\\varepsilon\\)-free indep
 endence and graph product von\nNeumann algebras\, including work of others
  and some of my own.\nParticular focus will be given to my recent joint wo
 rk with Jekel\,\nwhere we are able to use a 1969 result of Cartier and Foa
 ta on the\ncombinatorics of words as the key to describing the type I summ
 ands of\na graph product of von Neumann algebras.\n\nMC 5403
DTSTAMP:20260825T011953Z
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