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SUMMARY:Sam Kim
DTSTART:20200825T130000Z
DTEND:20200825T140000Z
DTSTAMP:20260423T035720Z
UID:GOBA/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GOBA/7/">Why
  MIP* = RE implies not-CEP and Blackadar-Kirchberg's MF problem</a>\nby Sa
 m Kim as part of Groups\, Operators\, and Banach Algebras Webinar\n\n\nAbs
 tract\nIn this expository talk\, we explain a direct route to why the resu
 lts of Ji\, Natarajan\, Vidick\, Wright\, and Yuen give us a II$_1$-factor
  that cannot embed into a tracial ultrapower of the separable hyperfinite 
 II$_1$-factor $\\mathcal{R}$. More specifically\, we define a class of fin
 itely generated unital C*-algebras $C^*(\\mathcal{G})$ for a fixed paramet
 er $\\mathcal{G}$ with the following property: there exist extremal traces
  $\\tau$ on $C^*(\\mathcal{G})$ such that the II$_1$-factor $\\mathcal{M}_
 \\tau$ generated by $C^*(\\mathcal{G})$ in the GNS representation of $\\ta
 u$ has the property that there cannot exist a unital *-homomorphism from $
 \\mathcal{M}_\\tau$ into a tracial ultrapower of $\\mathcal{R}$. We descri
 be ways in which convex geometry over $\\mathbb{R}^n$ will give us such pa
 rameters $\\mathcal{G}$ and extremal traces $\\tau$. As a consequence of o
 ur construction\, we have a separable counter-example of Blackadar-Kirchbe
 rg's MF problem\, which asks whether every stably finite C*-algebra embeds
  into a norm ultrapower of the UHF algebra $\\mathcal{Q}$. Questions relat
 ed to the refinement of both the MF conjecture and the refutation of CEP a
 re raised at the end.\n
LOCATION:https://researchseminars.org/talk/GOBA/7/
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