BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Camila Sehnem (Victoria University of Wellington) DTSTART:20220401T033000Z DTEND:20220401T043000Z DTSTAMP:20260423T052928Z UID:SiN/40 DESCRIPTION:Title: Equ ilibrium on Toeplitz extensions of higher dimensional noncommutative tori< /a>\nby Camila Sehnem (Victoria University of Wellington) as part of Symme try in Newcastle\n\n\nAbstract\nThe C*-algebra generated by the left-regul ar representation of $\\mathbb{N}^n$ twisted by a $2$-cocycle is a Toeplit z extension of an $n$-dimensional noncommutative torus\, on which each vec tor $r \\in [0\,\\infty)^n$ determines a one-parameter subgroup of the gau ge action. I will report on joint work with Z. Afsar\, J. Ramagge and M. L aca\, in which we show that the equilibrium states of the resulting C*-dyn amical system are parametrised by tracial states of the noncommutative tor us corresponding to the restriction of the cocycle to the vanishing coordi nates of $r$. These in turn correspond to probability measures on a classi cal torus whose dimension depends on a certain degeneracy index of the res tricted cocycle. Our results generalise the phase transition on the Toepli tz noncommutative tori used as building blocks in work of Brownlowe\, Haw kins and Sims\, and of Afsar\, an Huef\, Raeburn and Sims.\n LOCATION:https://researchseminars.org/talk/SiN/40/ END:VEVENT END:VCALENDAR