Mark Kac Seminar 2009-2010

February 5, 2010

introduction

talks

archive

contact

location

Location: Utrecht, Kromme Nieuwegracht 80, room 232

11:15-13:00	speaker: Yvan Velenik (Genève)	title: Ornstein-Zernike asymptotics in Statistical Mechanics
	abstract:  I'll review some recent applications of a general framework, loosely based on the renewal approach used by Ornstein and Zernike in the early XXth century, in order to obtain sharp asymptotics of various Statistical Mechanical quantities.  In particular, I'll discuss applications to:  (i) connectivities in subcritical random-cluster models (and the corresponding asymptotics for Ising/Potts correlation functions above the critical temperature),  (ii) interfaces in 2d Ising/Potts systems,  (iii) self-interacting polymers stretched by an external force.  I'll also describe the basic mathematical ideas in a simple case (probably the SAW).  This is based on joint works with M. Campanino and D. Ioffe.. Additional material: The slides of this lecture.
14:15-16:00	speaker: Mike Keane (Wesleyan University)	title: Orbits
	abstract: When one makes computer pictures of successive states or observations of a dynamical system, the information concerning their time ordering is usually lost. Therefore it is conceivable that different systems produce the same sets of pictures. Mathematically, we say in this case that the systems are orbit equivalent. In this lecture I shall discuss this phenomenon, describing the original classical work of Dye in the 1950's dealing with measure-theoretic orbit equivalence, the recent continuation initiated in 2004 by Hamachi and myself concerning finitary orbit equivalence, the topological orbit equivalence theory of Giordano, Putnam, and Skau from the 1990's, and the recent developments in 2009 around the yet open questions concerning finitary Kakutani equivalence due to Dykstra and Rudolph. I shall try to make the lecture accessible to a broad audience; although the techniques are complicated and the proofs lengthy, the basic ideas are relatively easy to grasp and may turn out to be useful elsewhere.

Mark Kac Seminar 2009-2010

last updated: 22 sep 2009 by Markus