Upcoming talks Summer 2021 Organizers
Archive:   Spring 2021   Fall 2020   Summer 2020

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 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

  • Apr 21
    Doug Hardin (Vanderbilt U)
    Asymptotics of periodic minimal discrete energy problems
    For $s>0$ and a lattice $L$ in $R^d$, we consider the asymptotics of $N$-point configurations minimizing the $L$-periodic Riesz $s$-energy as the number of points $N$ goes to infinity. In particular, we focus on the case $0<s<d$ of long-range potentials where we establish that the minimal energy $E_s(L,N)$ is of the form $E_s(L,N)=C_0 N^2 + C_1 N^{1+s/d} +o(N^{1+s/d})$ as $N\to \infty$ for constants $C_0$ and $C_1$ depending only on $s$, $d$, and the covolume of $L$. This is joint work with Ed Saff, Brian Simanek, and Yujian Su.

  • Apr 28
    Shujie Kang (UT Arlington)
    On the rank of non-informationally complete Gabor POVMs
    We investigate Positive Operator Valued Measures (POVMs) generated by Gabor frames in $\mathbb{C}^d$. A complete (Gabor) POVM is one that spans the space $\mathbb{C}^{d^{2}}$ of $d\times d$ matrices. It turns out that being a complete Gabor POVM is a generic property. As a result, the focus of this talk will be on non-complete Gabor POVMs. We will describe the possible ranks of these Gabor POVMs, and derive various consequences for the underlying Gabor frames. In particular, we will give details in dimensions $4$ and $5$.

  • May 5
    Mario Ullrich (JKU Linz)
    Random matrices and approximation using function values
    We consider $L_2$-approximation of functions and want to compare the power of function values with the power of arbitrary linear information. Under mild assumptions on the class of functions, we show that the minimal worst-case errors based on function values decay at almost the same rate as those with arbitrary info, if the latter decay fast enough. Our results are to some extent best possible and, in special cases, improve upon well-studied point constructions, like sparse grids, which were previously assumed to be optimal. The proof is based on deep results on large random matrices, including the recent solution of the Kadison-Singer problem, and reveals that (classical) least-squares methods might be surprisingly powerful in a general setting.

  • 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.

    Date Time Speaker Affiliation Title
    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 The spherical ensemble with external sources
    Feb 17 10am CST/11am EST/5pm CET Alex Iosevich U of Rochester Finite point configurations and frame theory
    Feb 24 10am CST/11am EST/5pm CET Kasso Okoudjou Tufts U Completeness of Weyl-Heisenberg POVMs
    Mar 3 10am CST/11am EST/5pm CET Mircea Petrache PUC Chile Sharp isoperimetric inequality, discrete PDEs and semidiscrete optimal transport
    Mar 10 *9:30am CST/10:30am EST/4:30pm CET Yeli Niu U of Alberta Discretization of integrals on compact metric measure spaces
    Daylight Saving Time in the US
    Mar 17 *12pm CDT/1pm EDT/6pm CET Xuemei Chen UNC Wilmington Frame Design Using Projective Riesz Energy
    Mar 24 10am CDT/11am EDT/4pm CET Ruiwen Shu U of Maryland Dynamics of Particles on a Curve with Pairwise Hyper-singular Repulsion
    Daylight Saving Time in Europe
    Mar 31 10am CDT/11am EDT/5pm CEST Oleg Musin U of Texas Rio Grande Valley Majorization, discrete energy on spheres and f-designs
    Apr 7 10am CDT/11am EDT/5pm CEST Woden Kusner U of Georgia Measuring chirality with the wind
    Apr 14 10am CDT/11am EDT/5pm CEST Peter Dragnev Purdue Fort Wayne Bounds for Spherical Codes: The Levenshtein Framework Lifted
    Apr 21 10am CDT/11am EDT/5pm CEST Doug Hardin Vanderbilt U Asymptotics of periodic minimal discrete energy problems
    Apr 28 *1pm CDT/2pm EDT/8pm CEST Shujie Kang UT Arlington On the rank of non-informationally complete Gabor POVMs
    May 5 *9:15am CDT/10:15am EDT/4:15pm CEST Mario Ullrich JKU Linz Random matrices and approximation using function values
    May 12 TBA William Chen Macquarie U TBA
    May 19 10am CDT/11am EDT/5pm CEST Johann Brauchart TU Graz TBA

    Summer 2021

    Date Time Speaker Affiliation Title
    Jun 9 TBA Alan Legg Purdue Fort Wayne TBA
    Jun 16 TBA Assaf Goldberger Tel Aviv U TBA
    Jun 23 TBA Hans Parshall Western Washington U TBA
    Jun 30 TBA Robert McCann UToronto TBA
    Jul 7 TBA Alexander McDonald U of Rochester TBA
    Jul 14 TBA Giuseppe Negro U of Birmingham TBA
    Jul 21 TBA Jonathan Passant U of Rochester TBA


    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