Permanents, matchings and van der Waerdens conjecture.

In 1926 van der Waerden conjectured that the minimum value of the permanent of a doubly stochastic matrix is $\frac {n!}{n^n}$.  This was proved by Egorychev and Falikman in 1980. Their proofs used special  case of Alexandorff-Fenchel inequalities. In this talk we will see an outline of a very simple proof using hyperbolic polynomials (due to Leonid Gurvits, 2008) and its applications in various graph matching counting problems. 
[This colloquium is meant for the VSRP students].