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SUMMARY:Raphael Ponge (Sichuan University)
DTSTART:20220330T190000Z
DTEND:20220330T200000Z
DTSTAMP:20260420T052740Z
UID:NYC-NCG/92
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/92/"
 >Dixmier trace formulas and negative eigenvalues of Schroedinger operators
  on noncommutative tori</a>\nby Raphael Ponge (Sichuan University) as part
  of Noncommutative geometry in NYC\n\n\nAbstract\nIn this talk\, we shall 
 first address a question raised by Alain Connes during a conference at Fud
 an University in Shanghai in 2017. We will also explain a link that has co
 me to light only recently between noncommutative geometry and the work of 
 Birman-Solomyak on semiclassical analysis of Schroedinger operators in the
  70s. We will then present results obtained jointly with Ed McDonald (UNSW
 -Sydney) on Cwikel-type estimates on NC tori. As an application we obtain 
 a version of Connes' integration formulas under very weak assumptions.  Fu
 rther applications include versions of the Cwikel-Lieb-Rozenblum and Lieb-
 Thirring inequalities for negative eigenvalues of Schroedinger operators o
 n noncommutative tori. Ultimately\, we get a seminclassical Weyl law for c
 urved noncommutative tori\, i.e.\, NC tori endowed with arbitrary Riemanni
 an metrics.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/92/
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