Oxford Mathematician Francis Bischoff talks about his recent work on generalized Kähler geometry and the problem of describing its underlying degrees of freedom.
Calibrated geometry, more specifically Calabi-Yau geometry, occupies a modern, rather sophisticated, cross-roads between Riemannian, symplectic and complex geometry. We will show how, stripping this theory down to its fundamental holomorphic backbone and applying ideas from classical complex analysis, one can generate a family of purely holomorphic invariants on any complex manifold. We will then show how to compute them, and describe various situations in which these invariants encode, in an intrinsic fashion, properties not only of the given manifold but also of moduli spaces.
Interest in these topics, if initially lacking, will arise spontaneously during this informal presentation.
Oxford Mathematician Weijun Xu talks about his exploration of the universal behaviour of large random systems:
"Nature comes with a separation of scales. Systems that have apparently different individual interactions often behave very similarly when looked at from far away. This phenomenon is particularly attractive when randomness is involved.
