Math Club: "Proving Pick's Theorem Using Erhart Theory"

Tu Pham, UCR

Monday, March 5, 2012
  4:10–5 p.m.

Location: Surge Building 284
  Parking Information

Category: Seminar

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Description: Given an integral polytope P in the plane, Pick's Theorem provides a simple formula to compute the area A of of this polytope, A = i (b/2) -1 where i  is the number of lattice points in the interior of P and b is the number of lattice points on the boundary of P. Ehrhart theory states that the function for counting the number of lattice points in an integral polytope of d-dimensions is a polynomial of degree d, and we call this polynomial the Ehrhart polynomial. We will introduce Ehrhart theory and a reciprocity theorem which will help us prove Pick's Theorem. If time permits, we will show examples of how to compute the Ehrhart polynomial of certain polytopes by using generating function.

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Open to: Students and Graduate Students Only
Admission: Free
Sponsor: Mathematics

Contact Information:
James Marberry

jamesm@math.ucr.edu