This weekly seminar will cover topics related to point distributions, potential and discrepancy theory, and adjacent areas. The target audience is young researchers working in the listed directions, but everyone is welcome! Please share this information with anyone interested.

We meet on Wednesdays, at 10am CDT/11am EDT/5pm CEST. To join the seminar via Zoom, follow the link. It becomes active half an hour before the meeting. To join our mailing list, go here.

Previous talks are available in the Archive.

#### Coming up

• July 28
Fátima Lizarte (University of Cantabria)
A sequence of well conditioned polynomials
In 1993, Shub and Smale posed the problem of finding a sequence of univariate polynomials $P_N$ of degree $N$ with condition number bounded above by $N$. In this talk, we show the origin of this problem, previous knowledge until this work, its relation to other interesting mathematical problems such as Smale's 7th problem, and our main result obtained: a simple and direct answer to the Shub and Smale problem for $N=4M^2$, with $M$ a positive integer, as well as comments on its proof.

This is a joint work with Carlos Beltrán.

Slides: [pdf]

• Aug 4
Jordi Marzo (University of Barcelona)
Quadrature rules, Riesz energies, discrepancies and elliptic polynomials
I will talk about the relation between optimal quadratures, Riesz (or logarithmic) energies and minimal discrepancy configurations. In particular I will discuss the use of the zeros of elliptic (or Kostlan-Shub-Smale) polynomials, among other configurations, as quadrature nodes for Sobolev spaces on the sphere. There will be many open problems throughout the talk.

• ## Schedule and speakers

The schedule is given in the local time for CST (Chicago) / EST (New York) / CET (Paris, Berlin) time zones; during daylight saving time it remains 10am/11am/5pm, respectively.

 Time Speaker Affiliation Title Date Jun 2 *11:30am CDT/12:30pm EDT/6:30pm CEST Austin Anderson and Alex White Florida State Asymptotics of Best Packing and Best Covering Jun 9 10am CDT/11am EDT/5pm CEST Alan Legg Purdue Fort Wayne Logarithmic Equilibrium on the Sphere in the Presence of Multiple Point Charges Jun 16 10am CDT/11am EDT/5pm CEST Assaf Goldberger Tel Aviv U Configurations, Automorphisms and Cohomology Jun 30 10am CDT/11am EDT/5pm CEST Robert McCann UToronto Maximizing the sum of angles between pairs of lines in Euclidean space Jul 7 10am CDT/11am EDT/5pm CEST Giuseppe Negro U of Birmingham Intermittent symmetry breaking for the maximizers to the Agmon-Hörmander estimate on the sphere Jul 14 10am CDT/11am EDT/5pm CEST Alexander McDonald U of Rochester Volumes spanned by k-point configurations in $\mathbb R^d$ Jul 21 10am CDT/11am EDT/5pm CEST Jonathan Passant U of Rochester Configurations and Erdős style distance problems Jul 28 10am CDT/11am EDT/5pm CEST Fátima Lizarte U of Cantabria A sequence of well conditioned polynomials Aug 4 10am CDT/11am EDT/5pm CEST Jordi Marzo U of Barcelona Quadrature rules, Riesz energies, discrepancies and elliptic polynomials Aug 18 10am CDT/11am EDT/5pm CEST Damir Ferizović TU Graz TBA Aug 25 10am CDT/11am EDT/5pm CEST Aicke Hinrichs JKU Linz TBA

### Organizers

 Ryan Matzke U of Minnesota matzk053@umn.edu Tetiana Stepaniuk Universität zu Lübeck stepaniuk@math.uni-luebeck.de Alex Vlasiuk Florida State ovlasiuk@fsu.edu Previously: Damir Ferizović TU Graz damir.ferizovic@math.tugraz.at