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SUMMARY:Positivity is undecidable in products of free algebras - William S
 lofstra (University of Waterloo)
DTSTART:20241202T100000Z
DTEND:20241202T104000Z
UID:TALK218584@talks.cam.ac.uk
DESCRIPTION:For free *-algebras\, free group algebras\, and related algebr
 as\, it is possible to decide if an element is positive (in all representa
 tions) using results of Helton\, Bakonyi-Timotin\, Helton-McCullough\, and
  others. In this talk\, I'll discuss joint work with Arthur Mehta and Yumi
 ng Zhao showing that this problem becomes undecidable for tensor products 
 of this algebras. I'll also discuss how results of this type could be aide
 d by having a Higman embedding theorem for algebras with states\, as well 
 as work in progress on this question.\nThis research direction is inspired
  by the MIP*=RE theorem\, which can also be understood as showing that a d
 ecision problem for operator algebras is undecidable.
LOCATION:Seminar Room 1\, Newton Institute
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