Forthcoming Seminars › Seminar Series

Junior Geometry and Topology Seminar

Thu, 17/01/2008
11:00 		George Raptis (University of Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
Introduction to simple-homotopy theory
Thu, 24/01/2008
11:00 		Jeff Giansiracusa (University of Oxford) Junior Geometry and Topology Seminar Add to calendar SR2
The Nielsen realisation problem and K3 surfaces
The Nielsen realisation problem asks when a collection of diffeomorphisms, which form a group up to isotopy, is isotopic to a collection of diffeomorphisms which form a group on the nose. For surfaces this problem is well-studied, I'll talk about this problem in the context of K3 surfaces.
Thu, 31/01/2008
11:00 		Oscar Randal-Williams (University of Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
The Hopf invariant 1 problem
For continuous maps $ f: S^{2n-1} \to S^n $ one can define an integer-valued invariant, the so-called Hopf invariant. The problem of determining for which $ n $ there are maps having Hopf invariant one can be related to many problems in topology and geometry, such as which spheres are parallelisable, which spheres are H-spaces (that is, have a product), and what are the division algebras over $ \mathbb{R} $. The best way to solve this problem is using complex K-theory and Adams operations. I will show how all the above problems are related, give an introduction to complex K-theory and it's operations, and show how to use it to solve this problem.
Thu, 07/02/2008
11:00 		Martinus Kool (University of Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
Moduli of Equivariant and Invariant Sheaves on Toric Varieties
Extending work of Klyachko and Perling, we develop a combinatorial description of pure equivariant sheaves on an arbitrary nonsingular toric variety X. This combinatorial description can be used to construct moduli spaces of stable equivariant sheaves on X using Geometric Invariant Theory (analogous to techniques used in case of equivariant vector bundles on X by Payne and Perling). We study how the moduli spaces of stable equivariant sheaves on X can be used to explicitly compute the fixed point locus of the moduli space of all stable sheaves on X, i.e. the subscheme of invariant stable sheaves on X.
Thu, 14/02/2008
11:00 		João Costa (Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
Global coordinates for the domain of outer communications of axisymmetric and stationary black hole space-times.
The usual procedure to obtain uniqueness theorems for black hole space-times ("No Hair" Theorems) requires the construction of global coordinates for the domain of outer communications (intuitively: the region outside the black hole). Besides an heuristic argument by Carter and a few other failed attempts the existence of such a (global) coordinate system as been neglected, becoming a quite hairy hypothesis. After a review of the basic aspects of causal theory and a brief discussion of the definition of black-hole we will show how to construct such coordinates focusing on the non-negativity of the "area function".
Thu, 21/02/2008
11:00 		Steven Rayan (Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
The Birkhoff-Grothendieck Theorem
Thu, 06/03/2008
11:00 		Johannes Ebert (Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
Stacks and classifying spaces

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

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