Research lectures, seminars and events
The events listed in this area are research seminars, workshops and lectures hosted by Durham University departments and research institutes. If you are not a member of the University, but wish to enquire about attending one of the events please contact the organiser or host department.
|December 2019||February 2020|
Events for 30 January 2020
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The tautological ring of smooth fibre bundles with fibre M is the subring of the cohomology of BDiff(M) generated by the generalised Miller-Morita-Mumford classes, which are defined as fibre integrals of characteristic classes of the vertical tangent bundle. The fibrewise Euler class can be defined more generally for fibrations with Poincaré fibre X so that there is an analogous definition of the tautological ring of fibrations as the subring of the cohomology of Bhaut(X) generated by fibre integrals of powers of the fibrewise Euler class. I will discuss how to compute it using the well-studied algebraic models of fibrations from rational homotopy theory. Furthermore, I will show how one can extract obstructions to smoothing fibrations for some rationally elliptic manifolds.
The attractors of dissipative dynamics at the boundary of chaos often has universal geometry. The explanation for this universality comes from renormalization. There is a simple and powerful idea in related areas of physics: a change of coordinates leaves things essentially the same. This idea is at the heart of geometric universality at the boundary of chaos.