Forthcoming Seminars › Seminar Series

Algebraic and Symplectic Geometry Seminar

Tue, 20/01/2009
15:45 		Frances Kirwan (Oxford) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Non-reductive GIT
Tue, 27/01/2009
15:45 		Dominic Joyce (Oxford) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Hamiltonian stationary submanifolds of compact symplectic manifolds
Let $ (M,\omega) $ be a symplectic manifold, and $ g $ a Riemannian metric on $ M $ compatible with $ \omega $. If $ L $ is a compact Lagrangian submanifold of $ (M,\omega) $, we can compute the volume Vol$ (L) $ of $ L $ using $ g $. A Lagrangian $ L $ is called Hamiltonian stationary if it is a stationary point of the volume functional amongst Lagrangians Hamiltonian isotopic to $ L $. Suppose $ L' $ is a compact Lagrangian in $ {\mathbb C}^n $ which is Hamiltonian stationary and rigid, that is, all infinitesimal Hamiltonian deformations of $ L $ as a Hamiltonian stationary Lagrangian come from rigid motions of $ {\mathbb C}^n $. An example of such $ L' $ is the $ n $-torus $  \bigl\{(z_1,\ldots,z_n)\in{\mathbb C}^n:\vert z_1\vert=a_1, \ldots,\vert z_n\vert=a_n\bigr\} $, for small $ a_1,\ldots,a_n>0 $. I will explain a construction of Hamiltonian stationary Lagrangians in any compact symplectic manifold $ (M,\omega) $, which works by `gluing in' $ tL' $ near a point $ p $ in $ M $ for small $ t>0 $.
Tue, 03/02/2009
15:45 		Greg Berczi (Oxford) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Multidegrees of singularities
Tue, 10/02/2009
15:45 		Young-Houn Kiem (Seoul National University) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Moduli theoretic compactifications of the space of smooth rational curves
The space of smooth rational curves of degree d in projective space admits various moduli theoretic compactifications via GIT, stable maps, stable sheaves, Hilbert scheme and so on. I will discuss how these compactifications are related by explicit blow-ups and -downs for d<4.
Tue, 17/02/2009
14:15 		Jacob Rasmussen (Cambridge) Algebraic and Symplectic Geometry Seminar Add to calendar Higman Room
Flag varieties and the HOMFLY polynomial I
Khovanov homology is an invariant of knots in $ S^3 $. In its original form, it is a "homological version of the Jones polynomial"; Khovanov and Rozansky have generalized it to other knot polynomials, including the HOMFLY polynomial. The first talk will be an introduction to Khovanov homology and its generalizations.
Tue, 17/02/2009
15:45 		Jacob Rasmussen (Cambridge) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Flag varieties and the HOMFLY polynomial II
Khovanov homology is an invariant of knots in $ S^3 $. In its original form, it is a "homological version of the Jones polynomial"; Khovanov and Rozansky have generalized it to other knot polynomials, including the HOMFLY polynomial. In the second talk, I'll discuss how Khovanov homology and its generalizations lead to a relation between the HOMFLY polynomial and the topology of flag varieties.
Tue, 03/03/2009
15:45 		Brent Doran (Oxford) Algebraic and Symplectic Geometry Seminar Add to calendar L3
On stably rational varieties
Tue, 10/03/2009
15:45 		Ian Grojnowksi (Cambridge) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Almost local difference operators

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

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