BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ved Datar (Indian Institute of Science (IISc) Bangalore) DTSTART:20200617T123000Z DTEND:20200617T133000Z DTSTAMP:20260513T204630Z UID:CMI/15 DESCRIPTION:Title: (In verse)-Hessian type equations and positivity in complex algebraic geometry \nby Ved Datar (Indian Institute of Science (IISc) Bangalore) as part of CMI seminar series\n\n\nAbstract\nIn the early 2000's Demailly and Paun proved that a (1\,1) cohomology class on a K\\"ahler manifold is positive if and only if certain intersection numbers are positive. This is a gener alization of the classical Nakai criteria for ampleness of line bundles on projective manifolds. The proof\, somewhat surprisingly\, relies on Yau's work on the complex Monge-Ampere equation\, and his solution to the Calab i conjecture. In 2019\, Gao Chen extended the method of Demailly-Paun to p rove that another important PDE in Kahler geometry\, namely the J-equation \, is equivalent to the positivity of certain (twisted) intersection numbe rs\, thereby settling a conjecture of Lejmi and Szekelyhidi. In my talk\, I will describe this circle of ideas\, concluding with a recent result obt ained in collaboration with Vamsi Pingali extending the work of Gao Chen t o more general inverse Hessian type equations\, thereby settling a conject ure of Szekelyhidi for projective manifolds. In the process we obtain an e quivariant version of Gao Chen's result\, and in particular recover some r esults of Collins and Szekelyhidi on the J-equation on toric manifolds.\n LOCATION:https://researchseminars.org/talk/CMI/15/ END:VEVENT END:VCALENDAR