### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**Matthew Russell**, Rutgers University, russell2 {at} math [dot] rutgers [dot] edu)
** Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: An Interesting Twist on the Classical Isoperimetric Problem

Speaker: **Anthony Zaleski**, Rutgers University

Date: Thursday, September 11, 2014 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

The isoperimetric problem asks: What region R of fixed area has least perimeter? Under appropriate assumptions, the answer is a ball. Here, we consider a "non-local" variation of this problem, in which the energy to be minimized consists of the perimeter plus ∫_{R} ∫_{R} |x-y|^{-a} dx dy, where a>0 is a constant parameter. The second, "repulsive" term suggests that nontrivial minimizers may now exist. In this talk, we focus on finding parameter regimes in which minimizers are still disks. Since our results follow from elementary calculus, geometric inequalities, and Maple computations, this talk should be accessible to all.

See: http://www.math.rutgers.edu/~russell2/expmath/