Past Colloquia

28 May 2004
16:30
Nigel Hitchin
Abstract
Einstein bequeathed many things to differential geometry — a global viewpoint and the urge to find new structures beyond Riemannian geometry in particular. Nevertheless, his gravitational equations and the role of the Ricci tensor remain the ones most closely associated with his name and the subject of much current research. In the Riemannian context they make contact in specific instances with a wide range of mathematics both analytical and geometrical. The talk will attempt to show how diverse parts of mathematics, past and present, have contributed to solving the Einstein equations.
30 January 2004
16:30
Doug Arnold
Abstract
Stability is central to the study of numerical algorithms for solving partial differential equations. But stability can be subtle and elusive. In fact, for a number of important classes of PDE problems, no one has yet succeeded in devising stable numerical methods. In developing our understanding of stability and instability, a wide range of mathematical ideas--with origins as diverse as functional analysis,differential geometry, and algebraic topology--have been enlisted and developed. The talk will explore the concept of stability of discretizations to PDE, its significance, and recent advances in its understanding.
28 November 2003
16:30
Abstract
A little more than 100 years ago, Issai Schur published his pioneering PhD thesis on the representations of the group of invertible complex n x n - matrices. At the same time, Alfred Young introduced what later came to be known as the Young tableau. The tableaux turned out to be an extremely useful combinatorial tool (not only in representation theory). This talk will explore a few of these appearances of the ubiquitous Young tableaux and also discuss some more recent generalizations of the tableaux and the connection with the geometry of the loop grassmannian.

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