Recently the recipients of Sloan Fellowships for 2012 has been announced. This is a kind grant/price awarded to young scientists, usually people who are assistant professors on the tenure track, from the U.S. and Canada. While the actual award is not exorbitant (but still large) the Sloan Fellowships seem to be a good indicator for further success in the career and, more importantly, for awaited breakthroughs by the fellows.

This year there are 20 mathematicians among the recipients and it appeared that I knew three of them:

• Rachel Ward (UTexas at Austin), a student of Ingrid Daubechies, has written a very nice PhD Thesis “Freedom through imperfection” on signal processing based on redundancy. Among several interesting works she has a very recent preprint Stable image reconstruction using total variation minimization which I plan to cover in a future post (according to the abstract the paper provides rigorous theory for exact recovery with discrete total variation which is cool).
• Ben Recht (University of Wisconsin, Madison) also works in the field of signal processing (among other fields) and is especially known for his work on exact matrix completion with compressed sensing techniques (together with Emmanuel Candes); I also liked his paper “The Convex Geometry of Linear Inverse Problems” (with Venkat Chandrasekaran, Pablo A. Parrilo, and Alan Willsky) with elaborated on the generalization of ${\ell^1}$-minimization and nuclear norm minimization.
• Greg Blekherman (Georgia Tech) works (among other things) on algebraic geometry and especially on the problem which non-negative polynomials (in more the one variable) can be written as sums of squares of polynomials, a question which is related to one of Hilbert’s 23 problems, namely Hilbert’s seventeenth problem. An interesting thing about non-negative polynomials and sums of squares is that: 1. Checking if a polynomial is non-negative is NP-hard. 2. Checking is a polynomial is a sum of squares can be done fast. 3. It seem that “most” non-negative polynomials are actually sums of squares but it unclear “how many of them”, see Greg’s chapter of the forthcoming book “Semidefinite Optimization and Convex Algebraic Geometry” here.

Congratulations!