Forthcoming Seminars › Seminar Series

Junior Geometry and Topology Seminar

Thu, 16/10/2008
12:00 		Oscar Randal-Williams (Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
Descent in algebra, geometry, and topology
Geometrically, the problem of descent asks when giving some structure on a space is the same as giving some structure on a cover of the space, plus perhaps some extra data. In algebraic geometry, faithfully flat descent says that if $ X\rightarrow Y $ is a faithfully flat morphism of schemes, then giving a sheaf on $ Y $ is the same as giving a collection of sheaves on a certain simplicial resolution constructed from $ X $, satisfying certain compatibility conditions. Translated to algebra, it says that if $ S\rightarrow R $ is a faithfully flat morphism of rings, then giving an $ S $-module is the same as giving a certain simplical module over a simplicial ring constructed from $ R $. In topology, given an etale cover $ X\rightarrow Y $ one can recover $ Y $ (at least up to homotopy equivalence) from a simplical space constructed from $ X $.
Thu, 06/11/2008
12:00 		Spiro Karigiannis (Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
Introduction to G_2 geometry (Part I)
I will give a survey-type introduction to manifolds equipped with $ G_2 $ structures, emphasizing the similarities and differences with Riemannian manifolds equipped with almost complex structures, and with oriented Riemannian 3-manifolds. Along the way I may discuss the Berger classification of Riemannian holonomy, the Calabi-Yau theorem, exceptional geometric structures arising from the algebra of the Octonions, and calibrated submanifolds. This talk will be in two parts.
Thu, 13/11/2008
12:00 		Spiro Karigiannis (Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
Introduction to G_2 geometry (Part II)
I will give a survey-type introduction to manifolds equipped with $ G_2 $ structures, emphasizing the similarities and differences with Riemannian manifolds equipped with almost complex structures, and with oriented Riemannian 3-manifolds. Along the way I may discuss the Berger classification of Riemannian holonomy, the Calabi-Yau theorem, exceptional geometric structures arising from the algebra of the Octonions, and calibrated submanifolds. This talk is the second of two parts.
Thu, 20/11/2008
12:00 		Alan Thompson (Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
The construction of ample <2>-polarised K3-fibrations
Fibrations are a valuable tool in the study of the geometry of higher dimensional algebraic varieties. By expressing a higher dimensional variety as a fibration by lower dimensional varieties, we can deduce much about its properties. Whilst the theory of elliptic fibrations is very well developed, fibrations by higher dimensional varieties, especially K3 surfaces, are only just beginning to be studied. In this talk I study a special case of the K3-fibration, where the general fibres admit a <2>-polarisation and the base of the fibration is a nonsingular curve.
Thu, 27/11/2008
12:00 		Martijn Kool (Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
Introduction to Deformation Theory
In this talk I will discuss some elementary notions of deformation theory in algebraic geometry like Schlessinger's Criterion. I will describe obstructions and deformations of sheaves in detail and will point out relations to moduli spaces of sheaves.
Thu, 04/12/2008
12:00 		Roberto Rubio (ICMAT Spain) Junior Geometry and Topology Seminar Add to calendar SR1
Hermitian G-Higgs bundles exceptionally flavoured
We introduce the notion of $ G $-Higgs bundle from studying the representations of the fundamental group of a closed connected oriented surface $ X $ in a Lie group $ G $. If $ G $ turns to be the isometry group of a Hermitian symmetric space, much more can be said about the moduli space of $ G $-Higgs bundles, but this also implies dealing with exceptional cases. We will try to face all these subjects intuitively and historically, when possible!

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

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