Past Colloquia

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>
28 May 2004
16:30
Nigel Hitchin
Abstract
Einstein bequeathed many things to differential geometry &mdash; 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.

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