March 2012

Bob Sturm’s list of 25 points for new PhD students is definitely worth reading. I am not sure if a PhD-starter can appreciate everything but at least in retrospect it is amusing and feels like someone has watching me during me PhD work…

A colleague of mine brought my attention to this course: Analysis, Modeling and Simulation of Collective Dynamics from Bacteria to Crowds to be held from July 9, 2012 to July 13, 2012 at the International Centre for Mechanical Sciences (CISM) in Udine, Italy. This is closely related to the topic I described in my previous post about models for consensus dynamics and related phenomena.

The abstract reads really interesting and the lists of topics includes

  • Kinetic models for self-organized collective motion.
  • Discrete and continuum dynamics of reacting and interacting individuals.
  • Finite-speed propagation models of chemo-tactic movements.
  • Modeling with measures.

Especially the last point catched my interest since I think that a proper model of “collective motion” should be done in measure spaces due to the inherent convergence to singular phenomena (in the case of collective motion the singularity will occur in velocity and not in space).

As another side remark, I was surprised to see that my former ZeTeM colleague Adrian Muntean is one of the organizers. It’s a pity that I can not join this course and would like to see notes of the planned lectures.

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.