Department of Mathematics                           University of Haifa
 
                      Special Topology & Geometry Seminar
 
Speaker: Prof. Michael Farber
         Durham University
 
Title:   Topology of linkages, statistical physics, and Morse theory
 
Date:    Tuesday, 21 December, 2010
 
Place:   Room 614 of the Science & Education Building, Univ. of Haifa
 
Time:    12:10
 
===>      NOTE SPECIAL  DAY!!! 
 
             Abstract
 
A topological approach to the theory of equilibrium phase transitions
in statistical physics is based on the Topological Hypothesis (TH), which
claims that phase transitions are due to changes of the topology of
suitable submanifolds in the configuration space. This approach was
widely discussed and tested in literature, in various models, with
positive and negative conclusions. In my talk I will consider the
anti-ferromagnetic mean-field XY model and study topology of the
sub-energy manifolds. The latter can be interpreted mechanically as
configuration space of a linkage with one telescopic leg. We use
methods of Morse theory to describe explicitly the Betti numbers of
this configuration space. We show that in the presence of an external
magnetic field the model undergoes a single "total Betti number phase
transition".
 
The talk is based on joint work with Viktor Fromm.
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: David Blanc   <blanc@math.haifa.ac.il>