### Weak limits of optimal discrete measures for Riesz potentials

- Series
- Analysis Seminar
- Time
- Wednesday, October 5, 2016 - 14:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Sasha Reznikov – Vanderbilt – aleksandr.b.reznikov@vanderbilt.edu

The problem in the talk is motivated by the following problem.
Suppose we need to place sprinklers on a field to ensure that every
point of the field gets certain minimal amount of water. We would like
to find optimal places for these sprinklers, if we know which amount of
water a point $y$ receives from a sprinkler placed at a point $x$; i.e.,
we know the potential $K(x,y)$. This problem is also known
as finding the $N$-th Chebyshev constant of a compact set $A$. We study
how the distribution of $N$ optimal points (sprinklers) looks when $N$
is large. Solving such a problem also provides an algorithm
to approximate certain given distributions with discrete ones. We
discuss connections of this problem to minimal discrete energy and to
potential theory.