BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexey Kuzmin (University of Gothenburg) DTSTART:20220615T190000Z DTEND:20220615T200000Z DTSTAMP:20260420T052725Z UID:NYC-NCG/103 DESCRIPTION:Title: Index theory of hypoelliptic operators on Carnot manifolds\nby Alexe y Kuzmin (University of Gothenburg) as part of Noncommutative geometry in NYC\n\n\nAbstract\nWe study the index theory of hypoelliptic operators on Carnot manifolds -- manifolds whose Lie algebra of vector fields is equipp ed with a filtration induced from sub-bundles of the tangent bundle. A Hei senberg pseudodifferential operator\, elliptic in the calculus of van Erp- Yuncken\, is hypoelliptic and Fredholm. Under some geometric conditions\, we compute its Fredholm index by means of operator K-theory. These results extend the work of Baum-van Erp (Acta Mathematica '2014) for co-oriented contact manifolds to a methodology for solving this index problem geometri cally on Carnot manifolds. Under the assumption that the Carnot manifold i s regular\, i.e. has isomorphic osculating Lie algebras in all fibres\, an d admits a flat coadjoint orbit\, the methodology derived from Baum-van Er p's work is developed in full detail. In this case\, we develop K-theoreti cal dualities computing the Fredholm index by means of geometric K-homolog y a la Baum-Douglas. The duality involves a Hilbert space bundle of flat o rbit representations. Explicit solutions to the index problem for Toeplitz operators and operators of the form "ΔH+γT" are computed in geometric K -homology\, extending results of Boutet de Monvel and Baum-van Erp\, respe ctively\, from co-oriented contact manifolds to regular polycontact manifo lds.\n LOCATION:https://researchseminars.org/talk/NYC-NCG/103/ END:VEVENT END:VCALENDAR