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. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: David Blanc <blanc@math.haifa.ac.il>