(2019.10.14 14:00pm N202)Richard P. Stanley:A survey of lattice polytopes

Time：2019-10-10 Source：

Title： A survey of lattice polytopes

Speaker： Richard P. Stanley (Department of Mathematics, MIT)

Time&Venue： 2019.10.14 14:00pm N202

Abstract:： Let P be a polygon in the plane with integer vertices. Suppose that the area of P is A and that P has I interior lattice points and B lattice points on the boundary. Alexander Pick showed that A=(2I+B-2)/2. What happens in higher dimensions? This question gave rise to a beautiful theory of lattice polytopes. We will survey some of the highlights of this theory, which is based on the Ehrhart polynomial of a lattice polytope and Ehrhart-Macdonald reciprocity. Several combinatorial applications will be given, as well as connections with commutative algebra.