Past Special Seminar

5 March 2009
Professor Bao Chau Ngo
<span lang="EN-GB"> <p> Derived direct image of a proper map with smooth source is a direct sum of simple perverse sheaves with shifts in the degrees. The supports of these simple perverse sheaves are obviously important  topological invariants of the map. In general, it is difficult to determine these supports. This is possible for an abelian fibration under some assumptions. This determination has some amazing  consequences on equality of number of points of certain algebraic varieties over finite fields and in particular, it implies the so called fundamental lemma in Langlands' program. </p> </span>
15 May 2007
Professor Michael Ward
A singular perturbation analysis is presented to analyze various PDE models in a two-dimensional domain that contain localized regions of non-uniform behavior. A key theme of this talk is to present a unified mathematical approach, based on an asymptotic analysis involving logarithmic series and certain Green's function techniques, that can be used to treat a variety of PDE models such as diffusion or eigenvalue problems in perforated domains or reaction-diffusion models with spot-type behavior.