MARK KAC SEMINAR
The seminar of 20032004: 
Main speaker 

October 10

Main speaker 20032004:
Our main speaker for this year is: (Institute of Analysis and Scientific Computing, School of Mathematics, EPFL, CH1015 Lausanne) The
first theory of condensation originated with the celebrated equation of state
of van der Waals. (p+a*v^{2})(vb)=RT. When
complemented with the Maxwell Construction (``equal area rule'') it leads
to isotherms describing general characteristics of the liquidvapor equilibrium.
The isotherms obtained with the van der WaalsMaxwell Theory have
a very simple analytic structure: they are analytic in a pure phase and have
analytic continuations along the liquid and gas branches, through the transition
points. These analytic continuations were originally interpreted as
describing the pressure of metastable states. The
first lecture will be devoted to the history of the problem,
to a precise
formulation of the results, as well as an exposition of PirogovSinai Theory,
which is the framework in which they are established. The
second lecture will be devoted to a detailed
proof of Isakov's theorem and
its generalization [1]. In the last lecture the results concerning the Kac limit γ to 0 will be presented [2]. I shall conclude with a discussion of important open problems. [1]
Friedli S., Pfister C.E., On the Singularity of the Free Energy at
First Order Phase Transition, to appear in Commun. Math. Phys. [2]
Friedli S., Pfister C.E., NonAnalyticity and the van der Waals
limit, to appear in J. Stat. Phys. [3]
Isakov S.N., Nonanalytic Features of the First Order Phase Transition in
the Ising Model}, Commun. Math. Phys. 95, 427443, (1984). [4]
Isakov S.N., Phase Diagrams and Singularity at the Point of a
Phase Transition of the First Kind in Lattice Gas Models,
Teoreticheskaya i Matematicheskaya
Fizika, 71, 426440, (1987). 

November
7 

November
28 

February
6


March
5 

March 26


May 7 

