## Simon Foucart## Associate Professor## Department of Mathematics## Texas A&M University |
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Current Research Activity:

Computational Approximation Theory in High Dimensions

(including Compressive Sensing)

- Classical Approximation Theory
- Sparse and Structured Recovery
- Scientific Computing
- Applications in Engineering and Bioinformatics

- Reading seminar on Compressive Sensing and Data Science (link)

- Students:
Mahmood Ettehad;
Bolong Ma;
Ryan Malthaner;
Srinivas Subramanian

Prospective - apply via the standard departmental process (link) - Postdocs:
Richard Lynch

Prospective - apply via mathjobs.org

S. F., H. Rauhut,
A mathematical introduction to compressive sensing.
Applied and Numerical Harmonic Analysis, Birkhäuser. List of errata |
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Approximation Theory XV: San Antonio 2016, Springer Proceedings in Mathematics & Statistics, vol 201, 61--104.

- I. Daubechies, R. DeVore, S. F., B. Hanin, G. Petrova, Nonlinear approximation and (deep) ReLU networks. (pdf)
- S. F., Sampling schemes and recovery algorithms for functions of few coordinate variables. (pdf) (reproducible)
- S. F., R. Gribonval, L. Jacques, H. Rauhut, Jointly low-rank and bisparse recovery: questions and partial answers. (pdf)
- M. Ettehad, S. F., Approximability models and optimal system identification. (pdf) (reproducible)
- S. F., J. B. Lasserre, Computation of Chebyshev polynomials for union of intervals. (pdf) (reproducible)

- D. Koslicki, S. F., G. Rosen,
Quikr: a method for rapid reconstruction of bacterial communities via compressive sensing.
(doi)
(pdf)

Bioinformatics, 29/17, 2096--2102, 2013. - S. F.,
Hard thresholding pursuit: an algorithm for compressive sensing.
(doi)
(pdf)

SIAM Journal on Numerical Analysis, 49/6, 2543--2563, 2011. - S. F., A. Pajor, H. Rauhut, T. Ullrich,
The Gelfand widths of $\ell_p$-balls for $0 < p \le 1$.
(doi)
(pdf)

Journal of Complexity, 26/6, 629--640, 2010. - S. F., M.-J. Lai,
Sparse recovery with pre-Gaussian random matrices.
(doi)
(pdf)

Studia Mathematica, 200, 91--102, 2010. - S. F., Yu. Kryakin, A. Shadrin,
On the exact constant in Jackson-Stechkin inequality for the uniform metric.
(doi)
(pdf)

Constructive Approximation, 29/2, 157--179, 2009.

**Topics in Mathematical Data Science**(in preparation)**Matrix Analysis**(a few lectures missing) (pdf)**Mathematics of Genome Analysis**(very incomplete, restricted access) (pdf)**Problem Solving Competitions**(selected topics) (pdf)**Compressed Sensing**(supplanted by the book written with H. Rauhut) (pdf)**Numerical Mathematics**(some updates required) (pdf)

Go to my Github page for download.

- MinProj
- This is a MATLAB package that computes exact projection constants and minimal projections in coordinate spaces and matrix spaces by solving linear programs, as well as approximate projection constants and minimal projections in polynomial spaces by solving linear or semidefinite programs. It relies on the external packages CVX and Chebfun.
- Basc
- This is a MATLAB package that computes Best Approximations by Splines under Constraints relative to various norms. Relying on the external packages CVX and Chebfun, it is based on a reformulation of constrained approximation problems as semidefinite programs. (demo)
- SplineDim
- This is a collection of SAGE routines designed to generate formulas for the dimension of multivariate spline spaces over specific partitions. It is based on Hilbert series computations. The core of the code was written by P. Clarke.
- Quikr and WGSQuikr
- These computational packages determine the composition of bacteria in an environmental sample analyzed by 16S rRNA amplicon and whole-genome shotgun sequencing technologies. The packages were assembled by D. Koslicki, who also set up this Galaxy server.
- HTP
- These are three MATLAB routines to be used when trying to recover a sparse vector x or a row-sparse matrix X from the incomplete linear measurements y=Ax or Y=AX. They are implementations of the HTP, FHTP, and SHTP algorithms.
- Allometry
- This is a collection of MATLAB routines to be used for the computation of exact constants in Banach space geometry.

- 2001-05: PhD, University of Cambridge.
- 2000-01: Part III of Math Tripos (Distinction), University of Cambridge.
- 1998-01: Masters of Engineering, Ecole Centrale Paris.

- 2015-now: Associate Professor of Mathematics, Texas A&M University.
- 2013-15: Assistant Professor of Mathematics, University of Georgia.
- 2010-13: Assistant Professor of Mathematics, Drexel University.
- 2009-10: Postdoctoral Researcher, University of Paris 6.
- 2006-09: Postdoctoral Researcher, Vanderbilt University.

- January-June 2019: University of Wisconsin-Madison.
- June 2018: LAAS-CNRS, Toulouse.
- December 2017: Hong Kong University of Science and Technology.
- May-June 2015: University of South Florida.
- July-August 2009: University of Bonn.

- 2012: Recipient of the Antelo Devereux Award for Young Faculty, Drexel University.
- 2010: Journal of Complexity Best Paper Award.

- Jean-Luc Bouchot (Nov 2012-Aug 2014, now Assistant Professor at Beijing Institute of Technology).
- David Koslicki (Jan-Sep 2012, now Assistant Professor at Oregon State University).
- Michael Minner (Sep 2012-Mar 2016, now at Sandia National Lab).

- Journal of Approximation Theory (Aug 2017-now).

Consultation hours: none in Spring 2019.

Office location:
502D Blocker Building

Ireland Street

College Station

Texas

Mailing address:
Texas A&M University

Department of Mathematics

3368 TAMU

College Station, TX 77843-3368

E-mail: foucart@tamu.edu or simon.foucart@centraliens.net