Date & Time: Wednesday, April 20, 2016, 16:00-17:00.
Venue: Ramanujan Hall
School of Mathematics, TIFR Mumbai
Title: Mori Program or Minimal Model Program (MMP) in Higher Dimension.
Abstract: Let X and Y be two algebraic varieties of dimension n. We say that X and Y are birationally equivalent if there exist non-empty open sets U of X and V of Y such that U is isomorphic to V as a variety. This forms an equivalence relation in the set of all varieties of a fixed dimension. Mori Program or Minimal Model Program (MMP) aims to find a 'minimal' variety in each of these equivalence classes. In this talk I will explain the algorithm of the Minimal Model Program and the challenges we face in higher dimensions compared to the surface case. If time permits I will also talk about the Singularities which appear in the MMP, and MMP in positive characteristic.