Dec/31/2012. Hoi Nguyen and I just finished our survey on Small ball probability and Inverse Littlewood-Offord theorems (to appear in the Erdos Centennial Volume). For a brief over view, see here.

I am organizing a summer school in Random Structures and Algorithms at VIASM (Vietnam Institue of Advanced Studies in Mathematics), in Hanoi (Vietnam) in July 2013. The instructors include M. Krisnapur, E. Welzl, HD. Phan, and myself. Here is the program schedule (see the bottom for information for applicants).

Aug/24/2013. Few weeks ago, Terence Tao and I posted a new paper on random polynomials on the arxiv. This paper addressed the local distributions of zeroes of a random polynomials, via a replacement principle. Among others, it gives answer to the classical question: How many real zeroes does a random polynomial have ? In special cases, the answer is known (such as Kac’s result), but the situation with the general case is far from settled, see this discussion for example. Among others, we show that the number of real roots do not depend on the distribution of the coefficients, once they share the same mean and variance (a two moment theorem). After this, one can replace all coefficients by gaussian variables and use Kac-Rice formula or Edelman-Kostlan method. See this link and this link for more details.

A revised version of SVD for finding hidden partitions. (March 2015).

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