(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.