Symplectic reduction is the natural quotient construction for symplectic manifolds. Given a free and proper action of a Lie group G on a symplectic manifold M, this process produces a new symplectic manifold of dimension dim(M) - 2 dim(G). For non-free actions, however, the result is usually fairly singular. But Sjamaar-Lerman (1991) showed that the singularities can be understood quite precisely: symplectic reductions by non-free actions are partitioned into smooth symplectic manifolds, and these manifolds fit nicely together in the sense that they form a stratification.

Symplectic reduction has an analogue in hyperkähler geometry, which has been a very important tool for constructing new examples of these special manifolds. In this talk, I will explain how Sjamaar-Lerman’s results can be extended to this setting, namely, hyperkähler quotients by non-free actions are stratified
spaces whose strata are hyperkähler.

Oxford Mathematics Public Lectures
Hooke Lecture

Michael Berry - Chasing the dragon: tidal bores in the UK and elsewhere
15 November 2018 - 5.15pm

In some of the world’s rivers, an incoming high tide can arrive as a smooth jump decorated by undulations, or as a breaking wave. The river reverses direction and flows upstream.

Understanding tidal bores involves

· analogies with tsunamis, rainbows, horizons in relativity, and ideas from  quantum physics;

· the concept of a ‘minimal model’ in mathematical explanation;

· different ways in which different cultures describe the same thing;

· the first unification in fundamental physics.

Michael Berry is Emeritus Professor of Physics, H H Wills Physics Laboratory, University of Bristol

5.15pm, Mathematical Institute, Oxford

Please email @email to register.

Watch live:

https://www.facebook.com/OxfordMathematics
https://livestream.com/oxuni/Berry

Oxford Mathematics Public Lectures are generously supported by XTX Markets.