BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jyotishman Bhowmick (Indian Statistical Institute\, Kolkata) DTSTART:20200513T101500Z DTEND:20200513T111500Z DTSTAMP:20260423T010753Z UID:MatPhySem/1 DESCRIPTION:Title: Formulation of metric compatibility of a connection in noncommutative ge ometry\nby Jyotishman Bhowmick (Indian Statistical Institute\, Kolkata ) as part of Mathematical Physics Seminar\n\n\nAbstract\nThe goal of the t alk is to formulate the notion of Levi-Civita connections in noncommutativ e geometry. More precisely\, we will work in the set up of differential ca lculus over a ( possibly ) noncommutative algebra. Given a pseudo-Riemann ian metric g on the calculus\, a connection on the space of one-forms will be called a Levi-Civita connection for g if the connection is torsionless and compatible with g. The torsion of a connection in noncommutative geo metry is well-known. So our main focus would be to define metric compatibi lity condition of a connection. We need the calculus to satisfy some condi tions to make sense of our metric compatibility condition and also the sym metry of the pseudo-Riemannian metric g. It turns out that these condition s are also sufficient to ensure the existence of a unique Levi-Civita conn ection for any bilinear pseudo-Riemannian metric. Examples of such calculu s include the fuzzy 3-sphere\, the quantum Heisenberg manifold and a class of Rieffel deformations of classical manifolds under free and isometric t oral actions. The talk is based on a joint work with D. Goswami and G. Lan di.\n LOCATION:https://researchseminars.org/talk/MatPhySem/1/ END:VEVENT END:VCALENDAR