Ed Saff as Pichorides Lecturer, May 2017

Our Department welcomes Prof Ed Saff, of Vanderbilt University, as a Pichorides Lecturer, in May 2017. The visit will take place from May 9 to May 31, 2017. Prof Saff will give lectures on

Discrete Minimal Energy on Rectifiable Sets

Summary: The six lectures will focus on the general topic of finding (computing) and analyzing configurations of points that are optimally or near-optimally distributed on a set. Such questions arise in a number of guises including best-packing problems, coding theory, geometrical modeling, statistical sampling, radial basis approximation, self-assembling materials, and even golf-ball design (i.e., where to put the indentations). Special emphasis will be given to the behavior (for large $N$) of $N$-point equilibrium configurations on a compact set $A$ for the Riesz potential $\Ds\frac{1}{r^s}$, where $s > 0$ is a parameter and $r$ denotes Euclidean distance between points. [The case $s=1$ in $\RR^3$ corresponds to the familiar Coulomb potential, while large $s$ corresponds (in the limit) to best-packing.] The analysis of such points falls under the umbrella of classical potential theory when $s < d=\text{dim}(A)$ and is a consequence of the continuous theory. But what if $s > d$ or $s = d$? In such cases, the classical theory does not apply and new techniques are needed to analyze the behavior of minimal energy configurations. We shall describe these techniques and related low-complexity techniques for computations. Connections will be made to the recently solved best-packing problems in $\RR^8$ and $\RR^{24}$.

The lectures are open to all and are mostly directed to graduate students and faculty of the Department. See also "Analysis Days 2017".

Schedule of the lectures (in Room A303):

Friday 12-5-2017, 11:15-1:00 (Lecture is here in PDF)
Wednesday 17-5-2017, 1:15-3:00 (Lecture is here in PDF)
Friday 19-5-2017, 11:15-1:00 (Lecture is here in PDF)

Information: Mihalis Kolountzakis