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.
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
Doug Hardin (Vanderbilt U)
Asymptotics of periodic minimal discrete energy problems
Abstract
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.
Shujie Kang (UT Arlington)
On the rank of non-informationally complete Gabor POVMs
Abstract
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 $5$.
Mario Ullrich (JKU Linz)
Random matrices and approximation using function values
Abstract
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
Organizers
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 |
|
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Previously: Damir Ferizović | TU Graz | damir.ferizovic@math.tugraz.at |