Approximation, sampling and compression in data science
ASC
3 January 2019 to 26 June 2019
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Programme theme
Approximation theory is the study of simulating potentially extremely complicated functions, called target functions, with simpler, more easily computable functions called approximants. The purpose of the simulation could be to approximate values of the target function with respect to a given norm, to estimate the integral of the target function, or to compute its minimum value. Approximation theory's relationship with computer science and engineering encourages solutions that are efficient with regards to computation time and space. In addition, approximation theory problems may also deal with real-life restrictions on data, which can be incomplete, expensive, or noisy. As a result, approximation theory often overlaps with sampling and compression problems.
The main aim of this programme is to understand and solve challenging problems in the high-dimensional context, but this aim is dual. On one hand, we would like to use the high-dimensional context to understand classical approximation problems. For example, recent developments have revealed promising new directions towards a break-through in a set of classical unsolved problems related to sampling in hyperbolic cross approximations. On the other hand, we want to understand why classical multivariate approximation methods fail in the modern high-dimensional context and to find methods that will be better and more efficient for modern approximation in very high dimensions. This direction will focus on two conceptual steps: First, replacement of classical smoothness assumptions by structural assumptions, such as those of sparsity used by compressed sensing. Second, the use of a nonlinear method, for instance a greedy algorithm, to find an appropriate sparse approximant.
In order to achieve the goal the programme will bring together researchers from different fields to work in groups on modern problems of high-dimensional approximation and related topics. It will foster exchange between different groups of researchers and practitioners.
The programme includes the following three workshops:
Workshop 1: Challenges in optimal recovery and hyperbolic cross approximation, February 18-22, 2019.
Workshop 2: Mathematics of data: structured representations for sensing, approximation and learning, May 28-31, 2019.
Workshop 3: Approximation, sampling, and compression in high dimensional problems, June 17-21, 2019.
Click here to download the programme's final scientific report
ASC programme: interview with organisers Vladimir Temlyakov and Anders Hansen
Preprints
| Title | Year | Programme |
|---|---|---|
LEBESGUE-TYPE INEQUALITIES IN GREEDY APPROXIMATIONAuthors: Stephen Dilworth, Gustavo Garrigos, Eugenio Hernandez, Denka Kutzarova, Vladimir Temlyakov |
2018 | ASC |
On the Extreme Zeros of Jacobi PolynomialsAuthors: Geno Nikolov |
2018 | ASC |
Wilkinson's bus: Weak condition numbers, with an application to singular polynomial eigenproblemsAuthors: Martin Lotz, Vanni Noferini |
2018 | ASC |
Delsarte's Extremal Problem and Packing on Locally Compact Abelian GroupsAuthors: Szilard Gy. Revesz, Elena Berdysheva |
2018 | ASC |
Delsarte's Extremal Problem and Packing on Locally Compact Abelian GroupsAuthors: Szilárd Gy Révészy, Elena Berdysheva |
2018 | ASC |
FIBONACCI LATTICES HAVE MINIMAL DISPERSION ON THE TWO-DIMENSIONAL TORUSAuthors: Simon Breneis, Aicke Hinrichs |
2018 | ASC |
EXTRA INVARIANCE OF PRINCIPAL SHIFT INVARIANT SPACES AND THE ZAK TRANSFORM.Authors: Eugenio Hernandez, Carolina Mosquera, Davide Barbieri |
2018 | ASC |
Sparse-grid polynomial interpolation approximation and integration for parametric and stochastic elliptic PDEs with lognormal inputsAuthors: Dũng Dinh |
2018 | ASC |
Greedy approximation for biorthogonal systems in quasi-Banach spacesAuthors: Pablo M. Berná, Przemyslaw Wojtaszczyk, Fernando Albiac, José Luis Ansorena |
2018 | ASC |
A remark on approximation with polynomials and greedy basesAuthors: Antonio Pérez, Pablo Manuel Berna |
2018 | ASC |
On the power of random informationAuthors: Erich Novak, Joscha Prochno, Mario Ullrich, David Krieg, Aicke Hinrichs |
2018 | ASC |
BASIS PROPERTIES OF THE HAAR SYSTEM IN LIMITING BESOV SPACESAuthors: Tino Ullrich, Gustavo Garrigos, Andreas Seeger |
2018 | ASC |
Workshops
Challenges in optimal recovery and hyperbolic cross approximation
18 February 2019 to 22 February 2019
The Mathematics of Deep Learning and Data Science
23 May 2019 to 23 May 2019
Mathematics of data: structured representations for sensing, approximation and learning
28 May 2019 to 31 May 2019
Approximation, sampling, and compression in high dimensional problems
17 June 2019 to 21 June 2019
Seminars
| Thursday 10th January 2019 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Peter Binev University of South Carolina |
Room 2 | |
| Friday 18th January 2019 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Andreas Seeger University of Wisconsin-Madison |
Room 2 | |
| Thursday 24th January 2019 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Elijah Liflyand Bar-Ilan University |
Room 2 | |
| Tuesday 29th January 2019 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Mikhail Tyaglov Shanghai Jiao Tong University |
Room 2 | |
| Monday 11th February 2019 | |||
|---|---|---|---|
| 15:00 to 16:30 |
Erich Novak Friedrich-Schiller-Universität Jena |
Room 1 | 
|
| Tuesday 12th February 2019 | |||
|---|---|---|---|
| 15:00 to 16:30 |
Ben Adcock Simon Fraser University |
Room 1 | |
| Wednesday 13th February 2019 | |||
|---|---|---|---|
| 15:00 to 16:30 |
Erich Novak Friedrich-Schiller-Universität Jena |
Room 1 |
|
| Thursday 14th February 2019 | |||
|---|---|---|---|
| 15:00 to 16:30 |
Ben Adcock Simon Fraser University |
Room 1 | |
| Friday 15th February 2019 | |||
|---|---|---|---|
| 15:00 to 16:30 |
Ben Adcock Simon Fraser University |
Room 1 | |
| Monday 25th February 2019 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Michael Lacey Georgia Institute of Technology |
Room 1 |
|
| Tuesday 12th March 2019 | |||
|---|---|---|---|
| 15:00 to 16:30 |
Elena Berdysheva Justus-Liebig-Universität Gießen |
Room 2 |
|
| Monday 25th March 2019 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Dorothee Haroske Friedrich-Schiller-Universität Jena |
Room 2 |
|
| Monday 8th April 2019 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Luz Roncal BCAM - Basque Center for Applied Mathematics |
Room 2 |
|
| Monday 29th April 2019 | |||
|---|---|---|---|
| 14:00 to 16:00 |
Yuan Xu University of Oregon |
Room 2 | |
| Wednesday 1st May 2019 | |||
|---|---|---|---|
| 13:00 to 14:45 |
Marta Betcke University College London |
Room 2 |
|
| Thursday 9th May 2019 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Nira Dyn Tel Aviv University |
Room 2 |
|
| Tuesday 21st May 2019 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Ronald DeVore Texas A&M University |
Room 1 |
|
| Friday 7th June 2019 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Guergana Petrova Texas A&M University |
Room 2 | |
| Wednesday 12th June 2019 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Svitlana Mayboroda University of Minnesota |
Room 1 |
|
| Thursday 13th June 2019 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Maria del Carmen Reguera Rodriguez University of Birmingham |
Room 2 | |
Organisers
- Anders Hansen University of Cambridge
- Alexei Shadrin University of Cambridge
- Vladimir Temlyakov University of South Carolina; Steklov Mathematical Institute, Russian Academy of Sciences
- Sergey Tikhonov ICREA and Universitat Autonoma de Barcelona; Centre de Recerca Matematica (CRM)
Speakers
- Ben Adcock Simon Fraser University
- Elena Berdysheva Justus-Liebig-Universität Gießen
- Marta Betcke University College London
- Peter Binev University of South Carolina
- Ronald DeVore Texas A&M University
- Nira Dyn Tel Aviv University
- Dorothee Haroske Friedrich-Schiller-Universität Jena
- Michael Lacey Georgia Institute of Technology
- Elijah Liflyand Bar-Ilan University
- Svitlana Mayboroda University of Minnesota
- Erich Novak Friedrich-Schiller-Universität Jena
- Guergana Petrova Texas A&M University
- Maria del Carmen Reguera Rodriguez University of Birmingham
- Luz Roncal BCAM - Basque Center for Applied Mathematics
- Andreas Seeger University of Wisconsin-Madison
- Mikhail Tyaglov Shanghai Jiao Tong University
- Yuan Xu University of Oregon
Participants
- Nina Gottschling Cambridge Centre for Analysis
- Ben Adcock Simon Fraser University
- Fernando Albiac Universidad Pública de Navarra
- Simon Arridge University College London
- Brad Baxter
- Daurenbek Bazarkhanov Institute of Mathematics and Mathematical Modeling
- Elena Berdysheva Justus-Liebig-Universität Gießen
- Pablo Manuel Berna Universidad Autonoma de Madrid
- Marta Betcke University College London
- Dmitriy Bilyk University of Minnesota
- Peter Binev University of South Carolina
- Thomas Blumensath University of Southampton
- Martin Buhmann Justus-Liebig-Universität Gießen
- Albert Cohen Université Pierre et Marie Curie Paris
- Feng Dai University of Alberta
- Mike Davies University of Edinburgh
- Alberto Debernardi Pinos Bar-Ilan University
- Ronald DeVore Texas A&M University
- Stephen Dilworth University of South Carolina
- Dũng Dinh Vietnam National University
- Oscar Dominguez Universidad Complutense de Madrid
- Pier-Luigi Dragotti Imperial College London
- Mikhail Dyachenko Lomonosov Moscow State University
- Nira Dyn Tel Aviv University
- Hans Feichtinger University of Vienna
- Simon Foucart Texas A&M University
- Gustavo Garrigos Universidad de Murcia
- Milana Gataric University of Cambridge
- Dmitry Gorbachev Steklov Mathematical Institute, Russian Academy of Sciences
- Karlheinz Groechenig University of Vienna
- Anupam Gumber Indian Institute of Science
- Anders Hansen University of Cambridge
- Dorothee Haroske Friedrich-Schiller-Universität Jena
- Eugenio Hernandez Universidad Autonoma de Madrid
- Aicke Hinrichs Johannes Kepler Universität
- Arieh Iserles University of Cambridge
- Valerii Ivanov Steklov Mathematical Institute, Russian Academy of Sciences
- Bill Johnson Texas A&M University
- Boris Kashin Steklov Mathematical Institute, Russian Academy of Sciences; Russian Academy of Sciences
- Gerard Kerkyacharian Université Denis Diderot; Université Paris 7 - Denis-Diderot
- Yurii Kolomoitsev Universität zu Lübeck
- Frances Kuo University of New South Wales
- Gitta Kutyniok Technische Universität Berlin
- Denka Kutzarova University of Illinois at Urbana-Champaign; Bulgarian Academy of Sciences
- Michael Lacey Georgia Institute of Technology
- Jeremy Levesley University of Leicester
- Elijah Liflyand Bar-Ilan University
- Martin Lotz University of Warwick
- Yuri Malykhin Steklov Mathematical Institute, Russian Academy of Sciences; Moscow State University
- Svitlana Mayboroda University of Minnesota
- Jason McEwen University College London
- Hrushikesh Mhaskar Claremont Graduate University
- Geno Nikolov Sofia University St. Kliment Ohridski
- Erich Novak Friedrich-Schiller-Universität Jena
- Yerlan Nursultanov Lomonosov Moscow State University
- Guergana Petrova Texas A&M University
- Gabriel Peyre CNRS - Ecole Normale Superieure Paris
- Dominique Picard Université Paris 7 - Denis-Diderot
- Clarice Poon University of Bath
- Jürgen Prestin Universität zu Lübeck
- Andriy Prymak University of Manitoba
- Holger Rauhut RWTH Aachen University
- Maria del Carmen Reguera Rodriguez University of Birmingham
- Justin Romberg Georgia Institute of Technology
- Luz Roncal BCAM - Basque Center for Applied Mathematics
- Konstantin Ryutin
- Thomas Schlumprecht Texas A&M University
- Andreas Seeger University of Wisconsin-Madison
- Alexei Shadrin University of Cambridge
- Teresa Signes Universidad de Murcia
- Ian Sloan University of New South Wales
- Thomas Strohmer University of California, Davis
- Jared Tanner University of Oxford
- Vladimir Temlyakov University of South Carolina; Steklov Mathematical Institute, Russian Academy of Sciences
- Laura Thesing University of Cambridge
- Sergey Tikhonov ICREA and Universitat Autonoma de Barcelona; Centre de Recerca Matematica (CRM)
- Damià Torres Latorre Universitat Politècnica de Catalunya
- Mikhail Tyaglov Shanghai Jiao Tong University
- Tino Ullrich Chemnitz University of Technology
- Ferenc Weisz Eötvös Loránd University
- Henryk Wozniakowski Columbia University; University of Warsaw
- Yuan Xu University of Oregon
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