Past Seminars › Seminar Series

Algebraic and Symplectic Geometry Seminar (past)

Tue, 30/06/2009
14:00 		Andrew Neitzke (Harcard) Algebraic and Symplectic Geometry Seminar Add to calendar L1
BPS wall-crossing, field theory and hyperkahler geometry
I will describe some recent joint work with Davide Gaiotto and Greg Moore, in which we explain the origin of the wall-crossing formula of Kontsevich and Soibelman, in the context of N=2 supersymmetric field theories in four dimensions. The wall-crossing formula gives a recipe for constructing the smooth hyperkahler metric on the moduli space of the field theory reduced on a circle to 3 dimensions. In certain examples this moduli space is actually a moduli space of ramified Higgs bundles, so we obtain a new description of the hyperkahler structure on that space.
Tue, 23/06/2009
15:45 		Ivan Smith (Cambridge) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Homological Mirror Symmetry for the 4-torus
I will describe joint work with Mohammed Abouzaid, in which we complete the proof of homological mirror symmetry for the standard four-torus and consider various applications. A key tool is the recently-developed holomorphic quilt theory of Mau-Wehrheim-Woodward.
Tue, 16/06/2009
14:00 		Joe Chuang (Bristol) Algebraic and Symplectic Geometry Seminar Add to calendar L1
Cubist algebras I
Tue, 26/05/2009
15:45 		Nicos Kapouleas (US) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Gluing constructions of special Lagrangian cones
I will survey the recent work of Haskins and myself constructing new special Lagrangian cones in $ {\mathbb C}^n $ for all $ n\ge3 $ by gluing methods. The link (intersection with the unit sphere $ {\cal S}^{2n-1} $) of a special Lagrangian cone is a special Legendrian $ (n-1) $-submanifold. I will start by reviewing the geometry of the building blocks used. They are rotationally invariant under the action of $ SO(p)\times SO(q) $ ($ p+q=n $) special Legendrian $ (n-1) $-submanifolds of $ {\cal S}^{2n-1} $. These we fuse (when $ p=1 $, $ p=q $) to obtain more complicated topologies. The submanifolds obtained are perturbed to satisfy the special Legendrian condition (and their cones therefore the special Lagrangian condition) by solving the relevant PDE. This involves understanding the linearized operator and its small eigenvalues, and also ensuring appropriate decay for the solutions.
Tue, 19/05/2009
15:45 		Kazushi Ueda (Oxford and Osaka) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Homological mirror symmetry for Brieskorn-Pham singularities
A polynomial $ f $ is said to be a Brieskorn-Pham polynomial if $  f = x_1^{p_1} + ... + x_n^{p_n} $ for positive integers $ p_1,\ldots, p_n $. In the talk, I will discuss my joint work with Masahiro Futaki on the equivalence between triangulated category of matrix factorizations of $ f $ graded with a certain abelian group $ L $ and the Fukaya-Seidel category of an exact symplectic Lefschetz fibration obtained by Morsifying $ f $.
Tue, 19/05/2009
14:00 		Ed Segal (Imperial College London) Algebraic and Symplectic Geometry Seminar Add to calendar L1
The closed state space of affine Landau-Ginzburg B-models
I'll define the category of B-branes in a LG model, and show that for affine models the Hochschild homology of this category is equal to the physically-predicted closed state space. I'll also explain why this is a step towards proving that LG B-models define TCFTs.
Thu, 07/05/2009
15:45 		Eduard Looijenga (Utrecht) Algebraic and Symplectic Geometry Seminar Add to calendar SR1
Vanishing cycles and Sebastiani-Thom in the setting of motivic integration II
This is an overview, mostly of work of others (Denef, Loeser, Merle, Heinloth-Bittner,..). In the first part of the talk we give a brief introduction to motivic integration emphasizing its application to vanishing cycles. In the second part we discuss a join construction and formulate the relevant Sebastiani-Thom theorem.
Thu, 07/05/2009
14:00 		Eduard Looijenga (Utrecht) Algebraic and Symplectic Geometry Seminar Add to calendar SR1
Vanishing cycles and Sebastiani-Thom in the setting of motivic integration I
This is an overview, mostly of work of others (Denef, Loeser, Merle, Heinloth-Bittner,..). In the first part of the talk we give a brief introduction to motivic integration emphasizing its application to vanishing cycles. In the second part we discuss a join construction and formulate the relevant Sebastiani-Thom theorem.
Tue, 28/04/2009
15:45 		Geordie Williamson (Oxford) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Some geometric constructions of link homology
Triply graded link homology (introduced by Khovanov and Rozansky) is a categorification of the HOMFLYPT polynomial. In this talk I will discuss recent joint work with Ben Webster which gives a geometric construction of this invariant in terms of equivariant constructible sheaves. In this framework the Reidemeister moves have quite natural geometric proofs. A generalisation of this construction yields a categorification of the coloured HOMFLYPT polynomial, constructed (conjecturally) by Mackay, Stosic and Vaz. I will also describe how this approach leads to a natural formula for the Jones-Ocneanu trace in terms of the intersection cohomology of Schubert varieties in the special linear group.
Tue, 10/03/2009
15:45 		Ian Grojnowksi (Cambridge) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Almost local difference operators
Tue, 03/03/2009
15:45 		Brent Doran (Oxford) Algebraic and Symplectic Geometry Seminar Add to calendar L3
On stably rational varieties
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, 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, 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.

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

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