Ed Saff as Pichorides Lecturer, May 2017

$ \newcommand{\Ds}{\displaystyle} \newcommand{\PP}{{\mathbb P}} \newcommand{\RR}{{\mathbb R}} \newcommand{\KK}{{\mathbb K}} \newcommand{\CC}{{\mathbb C}} \newcommand{\ZZ}{{\mathbb Z}} \newcommand{\NN}{{\mathbb N}} \newcommand{\TT}{{\mathbb T}} \newcommand{\QQ}{{\mathbb Q}} \newcommand{\Abs}[1]{{\left|{#1}\right|}} \newcommand{\Floor}[1]{{\left\lfloor{#1}\right\rfloor}} \newcommand{\Ceil}[1]{{\left\lceil{#1}\right\rceil}} \newcommand{\sgn}{{\rm sgn\,}} \newcommand{\Set}[1]{{\left\{{#1}\right\}}} \newcommand{\Set}[1]{{\left\{{#1}\right\}}} $

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

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".