2009 CMS Winter Meeting
University of Windsor, Windsor, Ontario, December 5 - 7, 2009

Coxeter-James Prize

Essential dimension for moduli stacks

Essential dimensions is a notion invented by Zinovy Reichstein and Joe Buhler to study the complexity of field extensions and, more generally, principal G bundles over a field. More generally, it can be thought of as a measure of the the complexity of algebraic objects defined over a field. Zinovy Reichstein, Angelo Vistoli and I developed techniques for studying the essential dimension of algebraic objects parametrized by stacks. For example, we can compute the essential dimension of the moduli stack of genus g curves. Roughly speaking this determines how many parameters it takes to define such a curve over a field.

I will discuss my work with Reichstein and Vistoli and the concept of essential dimension in general.

Event Sponsors

University of Windsor    Centre de recherches mathématiques Fields Institute MITACS Pacific Institute for the Mathematical Sciences

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