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SUMMARY:Supercritical phase transition for the ax+b monoid - Tyler Schulz 
 (University of Victoria)
DTSTART:20250703T100000Z
DTEND:20250703T102000Z
UID:TALK233770@talks.cam.ac.uk
DESCRIPTION:The seminal work of Bost and Connes has inspired a great deal 
 of interest in the KMS equilibrium states of C*-dynamical systems of numbe
 r theoretic origin. One such system is the Toeplitz algebra of the (right)
  ax+b monoid over the natural numbers N with natural dynamics\, first cons
 idered by an Heuf\, Laca and Raeburn\; they classified the KMS states of t
 his system at low temperatures and showed that the extremal states are par
 ametrized by points on the circle. I will present on my joint work with Ma
 rcelo Laca\, in which we complete the classification of KMS states and dem
 onstrate that the extremal KMS states at high temperatures are parametrize
 d by the 1-point compactification of N (equiv.\, by closed subgroups of th
 e circle). This is in contrast to the uniqueness of equilibrium at high te
 mperature observed in previously considered systems arising from number th
 eory. We also establish a connection between the phase transitions on quot
 ients of our system and the Bost-Connes phase transition.
LOCATION:External
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