Event

G-complete reducibility: Connecting algebra, geometry and representation theory

Dr Alastair Litterick (University of Essex)

  • Thu 19 Mar 20

    14:00 - 16:00

  • Colchester Campus

    STEM 3.1

  • Event speaker

    Dr Alastair Litterick

  • Event type

    Lectures, talks and seminars
    Mathematical Sciences Departmental Seminar

  • Event organiser

    Mathematical Sciences, Department of

  • Contact details

    Andrew Harrison

Mathematical Sciences Departmental Seminar

These Departmental Seminars are for everyone interested in Maths. We encourage anyone interested in the subject in general, or in the particular subject of the seminar, to come along. It's a great opportunity to meet people in the Maths Department and join in with our community. 

Refreshments are shared in the Department (STEM 5.1) after every seminar.

G-complete reducibility: Connecting algebra, geometry and representation theory

The notion of ‘complete reducibility’ is fundamental in representation theory and commutative algebra. Complete reducibility is responsible for many problems becoming easy to solve, for instance in finite group theory, geometry, Lie groups, Lie algebras and elsewhere.

Translating this concept into purely group-theoretic terms, J.P. Serre extended this notion to ‘G-complete reducibility’ in a reductive algebraic group G. It turns out that this allows many techniques and results from commutative algebra to be extended to the world of algebraic groups, and also has surprising connections to geometry, particularly affine Geometric Invariant Theory. We’ll take a look at these connections and some applications to abstract group theory.

Speaker

Dr Alastair Litterick is a Lecturer in Mathematics in the Department of Mathematical Sciences.

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