4/18 – Jennifer Li: Convex Reflexive Lattice Polygons and the Number 12

After the Annie’s talk last week (see below for the abstract!), we will enjoy some more combinatorics.

Jennifer will give a talk about “Convex Reflexive Lattice Polygons and the Number 12”, revealing how a simple equality can be connected to a deep result from another side of mathematics, which is called algebraic geometry. Here is her abstract:

A lattice polygon is a polygon with integral vertices in R^2. This means that its vertices are of the form (a, b), where a and b are integers. A reflexive lattice polygon has the property that the origin (0,0) is the unique integral interior point of the polygon. These polygons have duals, which are also reflexive lattice polygons. Today I will present a curious relation between convex reflexive lattice polygons, their duals, and the number 12. I will explain how this relation has deep connections with toric varieties, forming a bridge between two beautiful areas in mathematics: combinatorics and algebraic geometry.