Junior Geometry and Topology Seminar
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Thu, 15/10/2009 12:00 |
Dirk Schlueter (Oxford) |
Junior Geometry and Topology Seminar  |
SR1 |
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Thu, 22/10/2009 12:00 |
Alan Thompson (Oxford) |
Junior Geometry and Topology Seminar |
SR1 |
| A <2>-polarised K3 surface admits an embedding into weighted projective space defined by its polarisation. Let X be a family of such surfaces, then one can construct a projective model W of X such that the map from X to W realises this embedding on the general fibre. This talk considers what happens to W when we allow the fibres of the family X to degenerate. | |||
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Thu, 29/10/2009 12:00 |
George Raptis (Oxford) |
Junior Geometry and Topology Seminar |
SR1 |
| The talk is about the homotopy type of configuration spaces. Once upon a time there was a conjecture that it is a homotopy invariant of closed manifolds. I will discuss the strong evidence supporting this claim, together with its recent disproof by a counterexample. Then I will talk about the corrected version of the original conjecture. | |||
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Thu, 05/11/2009 12:00 |
Peter Arndt (Göttingen / Cambridge) |
Junior Geometry and Topology Seminar |
SR1 |
| The spectrum of the integers is an affine scheme which number theorists would like to complete to a projective scheme, adding a point at infinity. We will list some reasons for wanting to do this, then gather some hints about what properties the completed object might have. In particular it seems that the desired object can only exist in some setting extending traditional algebraic geometry. We will then present the proposals of Durov and Shai Haran for such extended settings and the compactifications they construct. We will explain the close relationship between both and, if time remains, relate them to a third compactification in a third setting, proposed by Toen and Vaquie. | |||
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Thu, 12/11/2009 12:00 |
Tom Baird (Oxford) |
Junior Geometry and Topology Seminar |
SR1 |
| I will survey the theory of quasiHamiltonian spaces, a.k.a. group valued moment maps. In rough correspondence with historical development, I will first show how they emerge from the study of loop group representations, and then how they arise as a special case of "presymplectic realizations" in Dirac geometry. | |||
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Thu, 19/11/2009 12:00 |
Richard Wade (Oxford) |
Junior Geometry and Topology Seminar |
SR1 |
| We describe John Stalling's method of studying finitely generated free groups via graphs and moves on graphs called folds. We will then discuss how the theory can be extended to study the automorphism group of a finitely generated free group. | |||
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Thu, 26/11/2009 12:00 |
Ana Ferreira (Oxford) |
Junior Geometry and Topology Seminar |
SR1 |
| We will present a self-contained introduction to gauge theory, self-duality and instanton moduli spaces. We will analyze in detail the situation of charge 1 instantons for the 4-sphere when the gauge group is SU(2). Time permitting, we will also mention the ADHM construction for k-instantons. | |||
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Thu, 03/12/2009 12:00 |
Martijn Kool (Oxford) |
Junior Geometry and Topology Seminar |
SR1 |
| Extending work of Klyachko, we give a combinatorial description of pure equivariant sheaves on a nonsingular projective toric variety X and construct moduli spaces of such sheaves. These moduli spaces are explicit and combinatorial in nature. Subsequently, we consider the moduli space M of all Gieseker stable sheaves on X and describe its fixed point locus in terms of the moduli spaces of pure equivariant sheaves on X. Using torus localisation, one can then compute topological invariants of M. We consider the case X=S is a toric surface and compute generating functions of Euler characteristics of M. In case of torsion free sheaves, one can study wall-crossing phenomena and in case of pure dimension 1 sheaves one can verify, in examples, a conjecture of Katz relating Donaldson–Thomas invariants and Gopakumar–Vafa invariants. | |||
