Forthcoming events in this series


Thu, 18 Oct 2007

12:00 - 13:00
SR1

Cartan connections and parabolic geometries

David Baraglia
(University of Oxford)
Abstract

Klein's famous lecture proposes that to study geometry we study homogeneous spaces ie study transformation groups acting on a space. E. Cartan found a generalization now known as "Cartan geometries", these are a curved generalization of homogeneous spaces, eg Riemannian manifolds are Cartan geometries modeled on {Euclidean group}/{orthogonal group}.

Topics for my talk will be

Cartan geometries / Cartan connections

Parabolic geometries - a special class of Cartan geometries

Examples - depending on how much time but I will probably explain conformal

geometry as a parabolic geometry

Thu, 11 Oct 2007

12:00 - 13:00
SR1

The Poincaré - Hopf index theorem

Oscar Randal-Williams
(Oxford)
Abstract

We will prove an extended Poincaré - Hopf theorem, identifying several invariants of a manifold $M$. These are its Euler characteristic $\chi(M)$, the sum $\sum_{x_i} ind_V(x_i)$ of indices at zeroes of a vector field $V$ on $M$, the self-intersection number $\Delta \cap \Delta$ of the diagonal $\Delta \subset M \times M$ and finally the integral $\int_M e(TM)$ of the Euler class of the tangent bundle.

Tue, 22 Nov 2005
17:00
SR2

tba

tba
Fri, 17 Jun 2005
14:00
SR2

TBA

Fanis Matsoukas
Fri, 10 Jun 2005
14:00
SR2

CANCELLED

Fonger Ypma
Fri, 03 Jun 2005
14:00
SR2

TBA

Liz Hanbury
Fri, 27 May 2005
14:00
SR2

TBA

Graham Hope
Tue, 24 May 2005
14:00
SR1

TBA

Oliver Nash
(Oxford)
Fri, 20 May 2005
14:00
SR2

Cancelled

Oliver Nash