SPEAKER: Nicole Lemire

TITLE: Essential Dimension

ABSTRACT: Essential Dimension is, roughly speaking, a measure of the degree of complexity of an algebraic or geometric object defined over a base field $k$. Given an algebraic or geometric object $X$ over an extension field $K$ of $k$, the essential dimension of $X$ is the least transcendence degree of a field of definition of $X$ over the base field $k$. It determines how many independent parameters are required to define $X$. Essential dimension was first introduced by Buhler and Reichstein as a numerical invariant of finite and then by Reichstein for algebraic groups. It was then generalised by Merkurjev into functorial language. We will give a survey of results on essential dimension focusing on that of finite and algebraic groups.