Variations on a theme of J.-P. Serre: Complete reducibility in groups, representations, buildings and geometric invariant theory

Variations on a theme of J.-P. Serre: Complete reducibility in groups, representations, buildings and geometric invariant theory

When studying modules or other algebraic objects, it is common to try and break things up and study the simple pieces. Complete reducibility asks the question: Under what conditions do these simple objects fully describe the object we started with? In representation theory this becomes: Under what condition is every module a direct sum of its irreducible factors? This question, which a priori has nothing to do with geometry, topology or combinatorics, turns out to have deep connections with all these other areas. In this talk we will look at these connections, and we will see how fundamental representation-theoretic results have analogues and generalisations in other areas of pure mathematics.

Speaker

Dr Alastair Litterick, University of Essex

How to attend

If not a member of the Dept. Mathematical Science at the University of Essex, you can register your interest in attending the seminar and request the Zoom’s meeting password by emailing Dr Jesus Martinez-Garcia