Forthcoming Seminars › Seminar Series

Algebraic and Symplectic Geometry Seminar

Tue, 25/10/2011
15:45 		Agnes Gadbled (Cambridge) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Exotic monotone Lagrangian tori
There exist two constructions of families of exotic monotone Lagrangian tori in complex projective spaces and products of spheres, namely the one by Chekanov and Schlenk, and the one via the Lagrangian circle bundle construction of Biran. It was conjectured that these constructions give Hamiltonian isotopic tori. I will explain why this conjecture is true in the complex projective plane and the product of two two-dimensional spheres.
Tue, 08/11/2011
15:45 		Vittoria Bussi (Oxford) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Donaldson-Thomas theory: generalizations and related conjectures
Generalized Donaldson-Thomas invariants $ \bar{DT}^\alpha(\tau) $ defined by Joyce and Song are rational numbers which 'count' both $ \tau $-stable and $ \tau $-semistable coherent sheaves with Chern character $ \alpha $ on a Calabi-Yau 3-fold X, where $ \tau $ denotes Gieseker stability for some ample line bundle on X. The theory of Joyce and Song is valid only over the field $ \mathbb C $. We will extend it to algebraically closed fields $ \mathbb K $ of characteristic zero. We will describe the local structure of the moduli stack $ \mathfrak M $ of coherent sheaves on X, showing that an atlas for $ \mathfrak M $ may be written locally as the zero locus of an almost closed 1-form on an étale open subset of the tangent space of $ \mathfrak M $ at a point, and use this to deduce identities on the Behrend function $ \nu_{\mathfrak M} $ of $ \mathfrak M $. This also yields an extension of generalized Donaldson-Thomas theory to noncompact Calabi-Yau 3-folds. Finally, we will investigate how our argument might yield generalizations of the theory to a even wider context, for example the derived framework using Toen's theory and to motivic Donaldson-Thomas theory in the style of Kontsevich and Soibelman.
Tue, 15/11/2011
15:45 		Raf Bocklandt (Newcastle) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Noncommutative mirror symmetry for punctured surfaces

A dimer model on a surface with punctures is an embedded quiver such that its vertices correspond to the punctures and the arrows circle round the faces they cut out. To any dimer model Q we can associate two categories: A wrapped Fukaya category F(Q), and a category of matrix factorizations M(Q). In both categories the objects are arrows, which are interpreted as Lagrangian subvarieties in F(Q) and will give us certain matrix factorizations of a potential on the Jacobi algebra of the dimer in M(Q).

We show that there is a duality D on the set of all dimers such that for consistent dimers the category of matrix factorizations M(Q) is isomorphic to the Fukaya category of its dual,  F((DQ)). We also discuss the connection with classical mirror symmetry.
Tue, 22/11/2011
15:45 		Alexei Oblomkov (Massachusetts) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Representation theory of DAHAs
In the talk I plan to overview several constructions for finite dimensional represenations of DAHA: construction via quantization of Hilbert scheme of points in the plane (after Gordon, Stafford), construction via quantum Hamiltonian reduction (after Gan, Ginzburg), monodromic construction (after Calaque, Enriquez, Etingof). I will discuss the relations of the constructions to the conjectures from the first lecture.
Tue, 29/11/2011
15:45 		Ben Davison (Université Paris Diderot - Paris 7) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Motivic DT invariants of the one loop quiver with potential
Thu, 01/12/2011
13:30 		Sara Pasquetti (Imperial) Algebraic and Symplectic Geometry Seminar Add to calendar Gibson 1st Floor SR
Topological strings and dualities from M5 branes (COW seminar)

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

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