BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gihyun Lee (Ghent University) DTSTART:20230920T190000Z DTEND:20230920T200000Z DTSTAMP:20260420T053237Z UID:NYC-NCG/135 DESCRIPTION:Title: $L_p$-bounds for pseudodifferential operators on curved noncommutative t ori\nby Gihyun Lee (Ghent University) as part of Noncommutative geomet ry in NYC\n\n\nAbstract\nIn the theory of pseudodifferential operators\, o ne of the most essential topics is the study of mapping properties of pseu dodifferential operators between various kinds of function spaces. The inv estigation of $L_p$-boundedness of pseudodifferential operators is particu larly important\, considering its consequences for the regularity and exis tence of solutions of PDEs.\n\nThe purpose of this talk is to discuss the counterpart of this problem on noncommutative tori. Noncommutative tori ar e the most intensively studied noncommutative spaces in noncommutative geo metry and arise in various parts of mathematics and mathematical physics. Pseudodifferential calculus on noncommutative tori was introduced in early 1980s by A. Connes\, and it has emerged as an indispensable tool in the r ecent study of differential geometry of noncommutative tori. Meanwhile\, J . Rosenberg introduced the notion of Riemannian metric on noncommutative t ori a decade ago. In this talk\, I will first recall the notion of a curve d noncommutative torus\, i.e.\, a noncommutative torus endowed with a Riem annian metric in the sense of J. Rosenberg. I will then show the boundedne ss of pseudodifferential operators on noncommutative $L_p$-spaces associat ed with the volume form induced by a Riemannian metric. Based on joint wor k with V. Kumar.\n LOCATION:https://researchseminars.org/talk/NYC-NCG/135/ END:VEVENT END:VCALENDAR