Monday, October 24, 2011
Seminaris - Konferenzzentrum
14:00 Rick Kenyon - Brown University (Providence)
15:00 Coffee Break
15:30 Anders Björner - Royal Institute of Technology (Stockholm)
16:30 Michael Joswig - TU Darmstadt
Lecture - 14:00
The dimer model is the probability model of random perfect matchings of a graph. Natural parameters are edge weights.
We show that the parameter space of dimer models (equivalently, the space of line bundles) on a bipartite graph on a torus has the structure of a ``cluster variety", and is equipped with a Poisson structure defining an integrable system. A complete set of commuting Hamiltonians can be given explicitly in terms of dimers. (Joint work with A. Goncharov)
Lecture - 15:30
The concept of connectivity is central in graph theory as well as in topology. Some measure of connectivity is often the crucial technical ingredient that drives proofs in topological combinatorics.
The intuitive notion of being connected has been extended in several ways. This circle of ideas will be briefly reviewed and some examples, thoughts, and modest results will be presented.
Lecture - 16:30
A split of a convex polytope is a non-trivial decomposition into two parts along a hyperplane which does not separate any edge of the polytope. The study of splits of polytopes is motivated by phylogenetic problems in algorithmic biology. In this talk we will explore the role of the splits among all (regular) polytopal subdivisions of a given polytope.