Departmental Colloquia

The Monomer-Dimer Problem is one of the major topics in Statistical Physics, Computational Geometry, and many other fields. The Bethe Approximation has been applied to the monomer-dimer problem as a heuristic since the late 1930s. In the last 10--15 years the Bethe Approximation has also become one of the main practical tools in Machine Learning, especially in inference on graphical models. Surprisingly, this practical tool also has amazing theoretical power: it has been used to get new lower bounds on the permanents of doubly-stochastic matrices. We use this new lower bound to prove Friedland's Lower Asymptotic Matching Conjecture. (A full statement of the conjecture appears within a longer version of this abstract at the URL below).

A central technique in earlier work on Friedland's Conjecture was the stable (a.k.a. hyperbolic, as in PDE theory) polynomial approach to obtain lower bounds on mixed derivatives. This technique was also used in 2008 to prove a unification of several earlier conjectures of Egorychev, Falikman, Schrijver, and van der Waerden. So we review the stable polynomial technique as we discuss and compare it to our more recent Bethe approximation approach.
Abstract

Abstract: A well-studied problem in topology is the Novikov conjecture. In this lecture, I will explain what the Novikov conjecture is, why it is interesting, and report recent progress on the conjecture and other related problems. This talk should be accessible to non-experts.

"From molecular dynamics to conformation dynamics in compuational drug design."

Abstract: he talk describes the novel approach of conformation dynamics as developed by the speaker and his former coworker Christof Schuette (now FU Berlin) together with their research groups. The method, meanwhile also called Markov state modelling, is meant to replace classical molecular dynamics. It requires much less computational effort and thus now makes computational drug design much easier. The talk starts with Hamiltonian trajectory evaluation and then tours through different mathematical subjects like identification of metastable conformations, Markov chain Monte Carlo methods, robust Perron cluster analysis, mesh-free discretization of transfer operators and construction of infinite generators as well as their efficient computation. Molecular examples will be inserted to illustrate the different mathematical aspects. Finally, a newly designed pain relief drug will be presented (in permitted detail) that led to two recent patents pending. An estimated computational comparison with ANTON, a special purpose supercomputer for molecular dynamics computations, will be given.