Home >
Publications >
Software >
Teaching >
Seminar >
Links >
Contact >

Laurent Demanet

Szego Assistant Professor

Mathematics
Stanford
Math
Applied Math
 
 
 

Welcome

My research fields are mathematical computing and applied analysis. Particular topics of interest include analysis and algorithms for wave propagation, the applied side of harmonic and microlocal analysis, sparse approximations, and inverse problems.

I recently obtained my PhD in applied mathematics from Caltech. My advisor was Emmanuel Candes. Previously, I studied mathematical engineering and theoretical physics at UCL in Belgium.

My research is funded in part by the National Science Foundation.

I currently have an opening for one intern.
What's new in Applied Math
  • Rejecta Mathematica is an experimental journal started recently by M. Wakin et al. where you can submit any math paper provided it has been rejected elsewhere before. You need to provide an open letter disclosing in full honesty the reasons for rejection. Link. November 2007.
  • A new preprint by D. Needell and R. Vershynin presents an elegant algorithmic solution to compressed sensing. In short, ``regularized orthogonal matching pursuit'' (ROMP) has the speed of matching pursuit and the convergence guarantees of ell-1 minimization. See their paper. August 2007. Update October 2007: J. Romberg has a clever primal-dual version of ell-1 minimzation for the Dantzig selector that offers similar complexity and convergence estimates.
  • The problem of adapting fast multipole ideas to the Helmholtz equation (high-frequency electromagnetic scattering) has received some attention lately. V. Rokhlin and coworkers have developed a low-complexity method, and more recently L. Ying and B. Engquist presented an extension based on multiscale directional ideas. See their paper. August 2007.
  • The Abel prize goes to S. Varadhan of the Courant Institute, for his contributions to the theory of large deviations. It is the second time for probabilists to be in the spotlight over the past year, after W. Werner's Fields medal. March 2007.
  • CMV: the unitary analogue of Jacobi matrices. R. Killip and I. Nenciu present a remarkable Householder algorithm for unitary matrices, where the reduction is not to a tridiagonal matrix as in the symmetric case, but to a CMV matrix (pentadiagonal with every other element equal to zero on the +2 and -2 diagonals). The algorithm has antecedents in the linear algebra literature (A. Bunse-Gerstner and L. Esner), but here the algorithm is only an offshoot of a much deeper analysis. Link added December 2006. The paper in CPAM.
  • Compressed sensing, also known as compressive sampling, has become fertile ground for research in signal-oriented applied math over the past two years. The main idea is to formulate inverse problems using an ell-1 regularization, and measurements in an "incoherent" basis, even for tasks that do not look like they require this kind of formulation. Recent applications include A/D conversion, one-pixel cameras, and sensor networks. Link added December 2006. Three resource webpages are L1-magic at Caltech, Sparselab at Stanford, and the CS page at Rice.

Disclaimer: this column will be forever incomplete, and has no ambition of being representative of the field. My views are my own. Older news are on the What was new page.