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DTSTART:20260308T070000
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DTSTART:20251102T060000
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DTSTART;TZID=America/Toronto:20260731T093000
SEQUENCE:0
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URL:https://uwaterloo.ca/pure-mathematics/events/phd-thesis-defense-erik-se
 guin-ulam-stability-quantum-groups
SUMMARY:PhD Thesis Defense | Erik Séguin | Ulam Stability for Quantum Grou
 ps\nand Noncommutative Dynamics
CLASS:PUBLIC
DESCRIPTION:ERIK SÉGUIN\, UNIVERSITY OF WATERLOO\n\n_Ulam Stability for Qu
 antum Groups and Noncommutative Dynamics_\n\nIn this talk\, we discuss var
 ious \"noncommutative\" extensions of\nclassical commutative phenomena. We
  focus on two particular cases of\nthis: representation stability for loca
 lly compact quantum groups\n(extending representation stability for classi
 cal locally compact\ngroups) and minimality for C*-dynamical systems (exte
 nding minimality\nfor topological flows). In the first part of the talk\, 
 we discuss the\nquestion of Ulam stability for approximate representations
  of locally\ncompact quantum groups. We show that compact quantum groups a
 nd\namenable discrete quantum groups are representation stable. In the\npr
 ocess\, we establish a partial stability result for general amenable\nloca
 lly compact quantum groups\, showing that if one imposes additional\nconst
 raints on the approximate representation in question then the\nassumption 
 of compactness or discreteness can be dispensed with. In\nthe second part 
 of the talk\, we discuss the notion of minimality for\nC*-dynamical system
 s. We show that the accepted definition is somewhat\nunsatisfactory as an 
 extension of its commutative counterpart from\nboth a topological dynamica
 l and an operator algebraic perspective and\npresent an alternative notion
  of an extension which rectifies these\nissues. We demonstrate that this a
 lternate notion also encodes\noperator algebraic structure which does not 
 appear to have a direct\ndynamical connection\, further motivating its stu
 dy. We outline various\ncharacterizations and extension properties for thi
 s notion and discuss\nits consequences.\n\nMC 2009
DTSTAMP:20260726T174800Z
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