UAlberta-PIMS Mathematics and Statistics Colloquium: Danny Ofek

Let C be a class of algebraic structures. For example, C could be a class of quadratic forms, field extensions or algebraic curves of a given genus. To measure the complexity of C, mathematicians ask a natural question: how many algebraically independent parameters are needed to define an object in C up to isomorphism? The lisa@pims.math.ca answer to this question is known as the essential dimension of the class and denoted ed(C). While the definition of ed(C) is highly intuitive, computing the exact essential dimension of various structures has proven to be a notoriously difficult problem. In this talk, I will provide a historical overview of the theory of essential dimension, and the modern algebro-geometric tools used to estimate it. No specialized prerequisites are necessary; the talk will be accessible to a general graduate student audience.