Friday, November 20, 2009
3:30 pm, MC 5158

Shmuel Friedland
University of Illinois

Matchings, permanents and their random approximations

The number of matchings in graphs, appears frequently in applications: the number of possible matchings of applicants to open positions, the monomer-dimer model in statistical mechanics. This number can be stated as a permanent or haffnian of the corresponding $0-1$ matrix, which is known to be $\#P$-complete problem. In this talk, for a general public, we discuss some deterministic estimates for permanents, their random approximations, and related quantities of infinite graphs arising in statistical mechanics, if time permits. We will mention a number of open problems.
This lecture is dedicated to my colleague and collaborator Uri N. Peled. He got his Ph.D. from University of Waterloo 1976, under the direction of the late Peter L. Hammer. Uri passed away after a long battle with the brain cancer on Thursday, September 3, 2009.
A variant of this lecture is available at http://www2.math.uic.edu/~friedlan/kthectbeam4.8.pdf.