# Workshop of the laboratory "High-dimensional approximation and applications" ("Sampling recovery and related problems"), 21 – 26 December 2021

We (Laboratory of High-Dimensional Approximation and Applications of the Lomonosov Moscow State University (MSU), Chemnitz Technical University, and Moscow Center of Fundamental and Applied Mathematics) are organizing an school/workshop on sampling recovery. The format is hybrid (online + Suzdal). We plan to have a 5 days school/workshop from December 21 (Tuesday) till December 26 (Sunday) of 2021. We plan to have a number of series of 2 lectures (1 hour each) on the topic accessible for students and contributed talks.

Join Zoom Meeting:

Lecture schedule (Moscow time, UTC+3 !):

Tuesday, December 21:

→ 10:00–10:45, **Alexei Shadrin**, "On cardinality of the lower sets and their universal discretization";

→ 10:45–11:30, **Jan Vybiral**, "Robust and efficient identification of neural networks", slides;

→ 11:45–12:30, **Kateryna Pozharska**, "Sampling recovery of multivariate functions in the uniform norm", slides.

**Break**

→ 15:00–16:00, **Erich Novak**, "Linear information versus function evaluations for \(L_2\)-approximation", slides;

→ 16:15–17:15, **Vladimir Temlyakov**, "Recovery in \(L_p\) norms", slides.

Wednesday, December 22:

→ 10:00–10:45, **Egor Kosov**, "Sampling discretization problem for \(L^1\) norm", slides;

→ 10:45–11:30, **Felix Bartel**, "Optimality of Cross-validation in Scattered Data Approximation", slides.

**Break**

→ 15:00–16:00, **Karlheinz Groechenig**, "From Marcinkiewicz-Zygmund inequalities to approximation theorems and
quadrature rules";

→ 16:15–17:15, **Mario Ullrich**, "\(L_2\)-approximation based on Gaussian information, function values or other information", Lecture 1;

→ 17:30–18:30, **Vladimir Temlyakov**, "Recovery and discretization", slides.

Thursday, December 23:

→ 10:00–10:45, **Glenn Byrenheid**, "Constructive sparse approximation based on sampling";

→ 10:45–11:30, **Lutz Kämmerer**, "A sample efficient sparse FFT for arbitrary frequency candidate sets in high dimensions".

**Break**

→ 15:00–16:00, **Albert Cohen**, "Optimal sampling in least-squares methods - theory and practice", Lecture 1, slides;

→ 16:15–17:15, **Albert Cohen**, "Optimal sampling in least-squares methods - theory and practice", Lecture 2;

→ 17:30–18:30, **Mark Iwen**, "Sparse Fourier Transforms on Rank-1 Lattices for the Rapid and Low-Memory Approximation of Functions of Many Variables + Generalizations".

Friday, December 24:

→ 10:00–10:45, **Irina Limonova**, "On sampling discretization in \(L_2\)", slides;

→ 10:45–11:30, **Stefan Kunis**, "A survey condition number estimates for multivariate nonequispaced Fourier matrices", video.

**Break**

→ 14:50–15:00, **Erich Novak**, "Announcement", slides;

→ 15:00–16:00, **Mario Ullrich**, "\(L_2\)-approximation based on Gaussian information, function values or other information", Lecture 2, slides;

→ 16:15–17:15, **David Krieg**, "Recovering Sobolev Functions: Optimal versus Given Samples", Lecture 1, slides.

Saturday, December 25:

→ 10:00–10:45, **Giovanni Migliorati**, "Adaptive approximation by weighted least squares";

→ 10:45–11:30, **Konstantin Rjutin, Yurii Malykhin**, "The recovery of ridge functions";

→ 11:45–12:30, **Michael Schmischke**, "High-dimensional interpretable approximation of functions with low effictive dimension".

**Break**

→ 15:00–16:00, **Tino Ullrich**, "Implications of the Kadison Singer solution to the recovery of functions - optimal subsampling of random information", Lecture 1, slides;

→ 16:00–17:00, **Tino Ullrich**, "Implications of the Kadison Singer solution to the recovery of functions - optimal subsampling of random information", Lecture 2;

→ 17:15–18:15, **David Krieg**, "Recovering Sobolev Functions: Optimal versus Given Samples", Lecture 2.

The conference was resheduled from 3-7 May to 21-26 December.

Organizers

Vladimir Temlyakov and Tino Ullrich

Program and organizing commitee:

→ V.N. Temlyakov (chair)

→ Tino Ullrich (chair)

→ A.P. Solodov

→ E.D. Kosov

→ B.S. Kashin

→ V.E. Podolskii

→ P.A. Borodin

→ O.S. Kudryavceva

→ I.V. Limonova

Contacts: