Some Aspects of Lattice Points in Polytopes


Professor Richard Stanley (MIT)
Wed January 29th 2020, 2:00pm
Bldg 380 380Y

Let P be a polygon in the plane with integer vertices. Suppose that the area of P is A and that 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 points in polytopes. After surveying the highlights of this theory, including connections with commutative algebra, we will discuss some recent work related to integrality, positivity, and period collapse.

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