BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Raphael Ponge (Sichuan University) DTSTART:20241106T200000Z DTEND:20241106T210000Z DTSTAMP:20260420T053410Z UID:NYC-NCG/180 DESCRIPTION:Title: Noncommutative geometry and semiclassical analysis\nby Raphael Ponge (Sichuan University) as part of Noncommutative geometry in NYC\n\n\nAbstr act\nIn this talk\, I will present new results regarding semiclassical Wey l’s laws in the setup of Connes’ noncommutative geometry. They provide precise asymptotics for the counting functions of Schroedinger operators under the semiclassical limit. This improves and simplifies previous resul ts of McDonald-Sukochev-Zanin. This provides a bridge between semiclassica l analysis and noncommutative geometry. Thanks to the Birman-Scwhinger pri nciple and old results of Birman-Solomyak this reduces to establishing var ious weak Schatten class properties for the operators at stake. This has a number of applications. We shall present two of them. First\, we recover previously known semiclassical Weyl’s laws on Euclidean domains and clos ed manifolds. These results were proved in 60s and 70s. However\, thanks to our setup\, they can be deduced results of Minakshisundaram and Pleijel on short time heat kernel asymptotics for Laplacians that were establishe d in the late 40s. Second\, we obtain semiclassical Weyl laws for noncommu tative tori for any dimension. These laws were conjectured by Ed McDonald and the speaker.\n LOCATION:https://researchseminars.org/talk/NYC-NCG/180/ END:VEVENT END:VCALENDAR