Monday, April 28, 2014 - 2:00pm - 2:50pm
Péter Csikvári (Massachusetts Institute of Technology)
In this talk I will survey some results on statistical properties of matchings of very large and infinite graphs. The main goal of the talk is to describe a few applications of a new concept called matching measure. These applications include new results on the number of (perfect) matchings in large girth graphs as well as simple new proofs of certain statistical physical theorems. This is joint work with various subsets of Miklós Abért, Péter E. Frenkel, Tamás Hubai and Gábor Kun.
Thursday, January 17, 2013 - 11:30am - 12:20pm
James Nolen (Duke University)
I will talk about solutions to an elliptic PDE with conductivity coefficient that varies randomly with respect to the spatial variable. It has been known for some time that homogenization may occur when the coefficients are scaled suitably. Less is known about fluctuations of the solution around its mean behavior. For example, if an electric potential is imposed at the boundary, some current will flow through the material. What is the net current? For a finite random sample of the material, this quantity is random.
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