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 will meet on Wednesdays, at 10am CST/11am EST/5pm CET. 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

• Feb 3
A large deviation principle for empirical measures
The main object of this talk will be a model of $n$ interacting particles at equilibrium. I will describe its macroscopic behavior as $n$ grows to infinity by showing a Laplace principle or, equivalently, a large deviation principle. This implies, in some cases, an almost sure convergence to a deterministic probability measure. Among the main motivating examples we may find Coulomb gases on Riemannian manifolds, the eigenvalue distribution of Gaussian random matrices and the roots of Gaussian random polynomials. This talk is based on arXiv:1703.02680.

Paper: [arXiv]

• Feb 10
Arno Kuijlaars (KU Leuven)
The spherical ensemble with external sources
The talk is based on joint work with Juan Criado del Rey.
We study a model of a large number of points on the unit sphere under the influence of a finite number of fixed repelling charges. In the large n limit the points fill a region that is known as the droplet. For small external charges the droplet is the complement of the union of a number of spherical caps, one around each of the external charges. When the external charges grow, the spherical caps will start to overlap and the droplet ondergoes a non-trivial deformation.
We explicitly describe the transition for the case of equal external charges that are symmetrically located around the north pole. In our approach we first identify a motherbody that, due to the symmetry in the problem, will be located on a number of meridians connecting the north and south poles. After projecting onto the complex plane, and undoing the symmetry, we characterize the motherbody by means of the solution of a vector equilibrium problem from logarithmic potential theory.

Paper: [arXiv]

• ## 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 Feb 3 10am CST/11am EST/5pm CET David Garcı́a-Zelada Aix-Marseille U A large deviation principle for empirical measures Feb 10 10am CST/11am EST/5pm CET Arno Kuijlaars KU Leuven TBA Feb 17 10am CST/11am EST/5pm CET Alex Iosevich U of Rochester TBA Feb 24 10am CST/11am EST/5pm CET Kasso Okoudjou Tufts U TBA Mar 3 10am CST/11am EST/5pm CET Mircea Petrache PUC Chile TBA Mar 10 10am CST/11am EST/5pm CET Yeli Niu U of Alberta TBA Daylight Saving Time in the US Mar 17 *12pm CDT/1pm EDT/6pm CET Xuemei Chen UNC Wilmington TBA Daylight Saving Time in Europe Apr 7 10am CDT/11am EDT/5pm CEST Woden Kusner U of Georgia TBA May 12 TBA William Chen Macquarie U TBA May 19 10am CDT/11am EDT/5pm CEST Johann Brauchart TU Graz 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