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Graduate Colloquium Series: Daniel Gulbrandsen

February 20 @ 3:30 pm - 4:30 pm

Pick’s Theorem and Applications to Restricted Integer Partition Functions

Daniel Gulbrandsen
University of Wisconsin-Milwaukee
PhD Graduate Student

“A point in R^n is called an integral point if all of its coordinates are integers. In R^2, Pick’s Theorem relates the area of a polygon P, whose vertices all have integer coordinates, to the number of integral points it contains with the formula A = i + B/2 – 1, where A is the area of the P, i is the number of integral points in the interior of P, and B is the number of integral points contained on the boundary of P.
Now imagine placing a polygon in R^3 so that all of its vertices have integer coordinates. Does there exist a formula (similar to Pick’s Theorem) that relates the area of a polygon in R^3 to the number of integral points it contains? In this talk we will derive such a formula, show how our formula is a generalization of Pick’s formula, and investigate applications of the formula to restricted integer partition functions”.

Details

Date:
February 20
Time:
3:30 pm - 4:30 pm
Event Category:

Venue

EMS Building, Room E424A
E424A; 3200 N Cramer St.
Milwaukee, WI 53211 United States
+ Google Map
Phone:
414-229-4836
Website:
www4.uwm.edu/letsci/math