Past Colloquia

24 February 2006
16:30
Professor Jean-Marc Gambaudo
Abstract
In the year 1858, Herman Ludwig Ferdinand von Helmholtz published in <em>Crelle's Journal</em> a deep and pioneering paper on vortex motions where the topological properties of vortex lines in a fluid motion were emphasised. This work has been a strong source of inspiration for P G Tait who settled down the foundation of knot theory and for H Poincare, the father of geometric theory of dynamical systems. As a matter of fact, by the end of the 19<sup>th</sup> century, three topics, <i>knots, flows and fluids</i> were closely related. In the last decades, the topic has been boosted by a series of new appealing problems and interesting results gathered under the name <i>Topological Methods in Hydrodynamics</i>. Our talk will start with a short trip around the pioneering works. Then we will focus on two essential recent topics:
21 October 2005
16:30
Abstract
The recent developments of Mathematical Physics have brought very new ideas about the nature of space . I will argue that we have to mix the methods of noncommutative geometry of Alain Connes with the prophetic views of Grothendieck about the so-called motives and their motivic Galois group .<br> The dream of a &quot;cosmic Galois group&quot; may soon become an established reality .<br> &nbsp;
10 June 2005
16:30
Abstract
I will give an expository account of Mathai, Melrose, and Singer [math.DG/0402329], explaining how to define the projective Dirac &quot;operator&quot; when the underlying manifold is neither spin nor spin_C, and how to define its analytic index which need not be an integer. Nevertheless, the usual index formulas apply. <i>Professor Singer will be admitted as honorary member of the London Mathematical Society just before his talk.</i>

Pages