BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Marina Prokhorova (Technion) DTSTART:20230222T200000Z DTEND:20230222T210000Z DTSTAMP:20260420T053037Z UID:NYC-NCG/123 DESCRIPTION:Title: Index theory of unbounded Fredholm operators\nby Marina Prokhorova ( Technion) as part of Noncommutative geometry in NYC\n\n\nAbstract\nIndex t heory for norm continuous families of bounded Fredholm operators was devel oped in the classical work of Atiyah\; its analog for self-adjoint operato rs was developed in the work of Atiyah and Singer. The index theory of ell iptic differential operators on closed manifolds is based on these classic al results: one can pass from operators of positive order to operators of zeroth order\, and such a transformation is continuous.\n\nHowever\, in ot her situations one needs to deal with weaker topologies on the space of un bounded operators. For example\, for elliptic boundary value problems on c ompact manifolds with boundary\, the graphs of corresponding unbounded ope rators depend continuously on parameter. The topology determined by passin g from a closed operator to its graph is called the graph topology. The ho motopy type of relevant spaces of unbounded Fredholm operators was determi ned by M. Joachim in 2003.\n\nMy talk is devoted to an index theory of gra ph continuous families of unbounded Fredholm operators in a Hilbert space. I will show how this theory is related to the classical index theory of b ounded Fredholm operators. The talk is based on my recent preprints arXiv: 2110.14359 and arXiv:2202.03337.\n LOCATION:https://researchseminars.org/talk/NYC-NCG/123/ END:VEVENT END:VCALENDAR