**Date & Time:** Wednesday, August 14, 2013, 16:00-17:30.

**Venue:** Room 216

**Title:** Invariant theory of classical groups

**Speaker:** Wilberd van der Kallen, Utrecht University

**Abstract:** We will discuss the invariant theory of classical groups in this
series. Let a group $G$ act linearly on a finite dimensional complex vector
space $V$. It is natural to ask for the $G$-invariant complex valued
polynomial functions on $V$. These functions form a ring in a natural way. The
two fundamental theorems in invariant theory of $G$ give generators for this
ring as a complex algebra and the relations amongst these generators. As
an example, the symmetric group $S_n$ acts by permuting a basis of $C^n$ and
the corresponding invariants are generated as a polynomial ring by the
elementary symmetric functions. So the generators are the elementary symmetric
functions and there are no relations amongst them. Our aim in this lecture
series is to understand the invariants for the natural action of $GL(V)$ on
$V$ and on related vector spaces. If there is time, we will also study the
analogous theorems for the orthogonal and symplectic groups.

This is the first lecture in the series of six lectures.