Simon Foucart

Professor

Presidential Impact Fellow

Department of Mathematics

Texas A&M University




Current Research Activity:
Computational Approximation Theory in High Dimensions
(including Compressive Sensing)

Research

Objective

Find, exploit, and create synergies between
  • Classical Approximation Theory
  • Sparse and Structured Recovery
  • Scientific Computing
  • Applications in Engineering and Bioinformatics

Activities

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

Group

Publications

Author profiles on Google Scholar and MathSciNet.

Book

    S. F., H. Rauhut, A mathematical introduction to compressive sensing.
Applied and Numerical Harmonic Analysis, Birkhäuser.
List of errata

Survey

S. F., Flavors of compressive sensing. (doi) (pdf) (reproducible)
Approximation Theory XV: San Antonio 2016, Springer Proceedings in Mathematics & Statistics, vol 201, 61--104.

Preprints

  1. S. F., D. Needell, R. Pathak, Y. Plan, M. Wootters, Weighted matrix completion from non-random, non-uniform sampling patterns. (arXiv)
  2. I. Daubechies, R. DeVore, S. F., B. Hanin, G. Petrova, Nonlinear approximation and (deep) ReLU networks. (pdf)
  3. S. F., Sampling schemes and recovery algorithms for functions of few coordinate variables. (pdf) (reproducible)
  4. M. Ettehad, S. F., Approximability models and optimal system identification. (pdf) (reproducible)

Selected Publications

  1. S. F., J. B. Lasserre, Determining projection constants of univariate polynomial spaces.
    Journal of Approximation Theory, 235, 74--91, 2018. (doi) (pdf)
  2. R. Baraniuk, S. F., D. Needell, Y. Plan, M. Wootters, Exponential decay of reconstruction error from binary measurements of sparse signals.
    IEEE Transactions on Information Theory, 63/6, 3368--3385, 2017. (doi) (pdf)
  3. 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.
  4. S. F., Hard thresholding pursuit: an algorithm for compressive sensing. (doi) (pdf)
    SIAM Journal on Numerical Analysis, 49/6, 2543--2563, 2011.
  5. 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.

Complete papers inventory

Teaching

Current courses

Some lecture notes

  • Topics in Mathematical Data Science (in preparation, restricted access) (pdf)
  • 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)

Complete courses inventory

  • at the University of Georgia (link)
  • at Drexel University (link)
  • at Vanderbilt University (link)

Software

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.

Vita

Full curriculum vitae available in pdf.

Education

  • 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.

Professional experience

  • 2019-now: Professor of Mathematics, Texas A&M University.
  • 2015-19: 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.

Visiting positions

  • 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.

Honors and Awards

  • 2019: Recipient of a Presidential Impact Fellowship, Texas A&M University.
  • 2012: Recipient of the Antelo Devereux Award for Young Faculty, Drexel University.
  • 2010: Journal of Complexity Best Paper Award.

Advisees

  • Richard G. Lynch (Aug 2016-Jun 2019), now Instructional Assistant Professor at Texas A&M University.
  • Jean-Luc Bouchot (Nov 2012-Aug 2014, now Assistant Professor at Beijing Institute of Technology).
  • David Koslicki (Jan-Sep 2012, now Associate Professor at Pennsylvania State University).
  • Michael Minner (Sep 2012-Mar 2016, now at Sandia National Lab).

Editorial Boards

Contact


Consultation hours: TR 10:50am-11:30am, W 1:20pm-2:00pm, and by appointment.

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