# Past Events

In 1948, Claude Shannon published a paper that simultaneously invented the field of information theory and more or less answered all its major questions. One of Shannon's key ideas was the introduction of the entropy function, defined by the mysterious expression –Σ…

Lisa Sauermann: On counting algebraically defined graphs

For many classes of graphs that naturally arise in discrete geometry, the edges of these graphs can defined using the signs of a given finite list of polynomials. We prove a general result counting the number of such algebraically…

Let s_n(M_n) denote the smallest singular value of an nxn random matrix M_n. We will discuss a novel combinatorial approach (in particular, not using either inverse Littlewood--Offord theory or net arguments) for proving statements of the following form for quite general random matrix models:…

The analysis of simple mixing schemes can call on all sorts of math from 'random transpositions' ( put n cards face down in a row on the table and randomly switch pairs). Group representations are useful. Now, 'comparison theory' (part of analysis) allows study of many different schemes. These…

A recent work by Mazzeo-Swoboda-Weiss-Witt describes a stratum of the frontier of the space of SL(2,C) surface group representations in terms of 'limiting configurations' which solve a degenerated version of Hitchin's equations on a Riemann surface. We interpret these objects in (a mapping…

Motion planning algorithms allow autonomous functioning of mechanical systems (robots). I will discuss purely topological problems inspired by the motion planning problem of robotics and will survey some recent results. In particular, I will describe properties of motion planning algorithms in…

Abstract

A classical problem in contact geometry asks us to classify the symplectic manifolds which fill a given contact manifold. For virtually overtwisted torus bundles over S^1, we use Menke's JSJ-type decomposition to reduce this classification to the same problem for lens spaces. This leads to a…