BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jianchao Wu (Texas A & M) DTSTART:20200624T190000Z DTEND:20200624T200000Z DTSTAMP:20260420T053047Z UID:NYC-NCG/10 DESCRIPTION:Title: The Novikov conjecture\, groups of diffeomorphisms\, and infinite dimensi onal nonpositively curved spaces\nby Jianchao Wu (Texas A & M) as part of Noncommutative geometry in NYC\n\n\nAbstract\nThe rational strong Novi kov conjecture is a prominent problem in noncommutative geometry. It impli es deep conjectures in topology and differential geometry such as the (cla ssical) Novikov conjecture on higher signatures and the Gromov-Lawson conj ecture on positive scalar curvature. Using C*-algebraic and K-theoretic to ols\, we prove that the rational strong Novikov conjecture holds for geome trically discrete subgroups of the group of volume preserving diffeomorphi sms of any closed smooth manifold. The crucial geometric property of these groups that we exploit is the fact that they admit isometric and proper a ctions on a type of infinite-dimensional symmetric space of nonpositive cu rvature called the space of $L^2$-Riemannian metrics. In fact\, our result holds for any discrete group admitting an isometric and proper action on a (possibly infinite-dimensional) nonpositively curved space that we call an admissible Hilbert-Hadamard space\; thus our result partially extends e arlier ones of Kasparov and Higson-Kasparov. This is joint work with Sherr y Gong and Guoliang Yu.\n LOCATION:https://researchseminars.org/talk/NYC-NCG/10/ END:VEVENT END:VCALENDAR