Conference - Teichmüller Theory in Higher Dimension and Mirror Symmetry

Monday 24th Tuesday 25thWenesday 26thThursday 27th Friday 28th
15h15 -16h15BorotReicheltVisit CastleCatanese
16h15 -16h45CoffeeCoffeeCoffee
16h45 -17h45SauvagetTeleman
20h Social dinner

Katia Amerik (Orsay):

Abstract: TBA

Gaetan Borot (Bonn): The ABCD of topological recursion

Abstract: Following a recent proposal of Kontsevich and Soibelman, we study the quantization of quadratic Lagrangians in $T^*V$ (by a procedure of topological recursion. I will describe 3 geometric sources of such (quantized) Lagrangians: Frobenius algebras, non-commutative Frobenius algebras, and spectral curves. In the latter case, Kontsevich-Soibelman topological recursion retrieves Eynard-Orantin topological recursion. Based on a joint work with Andersen, Chekhov and Orantin.

Fabrizio Catanese (Bayreuth): Teichmueller space and automorphisms

Abstract: The most well known case of Teichmueller space is the one of complex tori, which yield a connected component of $\mathcal{T}(T)$ isomorphic to an open set of a Grassmannian. I shall present some recent results, the first joint with Pietro Corvaja, on the Teichmueller space of Generalized Hyperelliptic manifolds. These are finite free quotients $X = T/G$ of a complex torus. Using an algebraic result which says that a cristallographic group has a unique natural affine representation, we can describe natural components for $\mathcal{T}(X)$, again open sets in suitable Grassmannian. I shall then describe some joitn work with Gromadski , on surfaces of general type with automorphisms acting trivially on cohomology, respectively trivially on rational but not on integral cohomology. For irregular surfaces conjecturally there are no nontrivial automorphisms isotopic to the identity.

Thomas Reichelt (Heidelberg) Non-affine Landau Ginzburg models and mirror symmetry

Abstract: I will explain a close relationship between GKZ hypergeometric systems after Gelfand, Kapranov and Zelevinsky, Gauss-Manin systems of families of Laurent polynomials and the intersection cohomology of hyperplane sections in a toric variety. As an application, I will show how to construct non-affine Landau-Ginzburg models which are mirror partners for complete intersections in toric varieties with a numerical effective anti-canonical divisor.

Claude Sabbah (Ecole Polytechnique):

Abstract: TBA

Adrien Sauvaget (Paris):Tautological rings with effective spin structures

Abstract: We introduce a family of subrings of the Chow rings of the moduli spaces of r-spin structures called the tautological rings with effective spin structures. These rings are an enrichment of the standard tautological rings with the classes of loci of effective spin structures. We will describe the product in these rings and explain how this presentation of the ring structure together with conjectures of Janda, Pandharipande, Pixton and Zvonkine should allow to compute intersections of Witten’s classes.

Jacopo Stoppa (SISSA):

Abstract: TBA

Andrei Teleman (Marseille):On the moduli stack of class VII surfaces

Abstract: The most important gap in the Kodaira-Enriques classification table concerns the Kodaira class VII, e.g. the class of surfaces $X$ having $\mathrm{kod}(X) =- \infty$, $b_1(X) = 1$.

The main conjecture which (if true) would complete the classification of class VII surfaces, states that any minimal class VII surface with $b_2 > 0$ contains $b_2$ holomorphic curves. A weaker conjecture states that any such surface contains a cycle of curves, and (if true) would complete the classification up to deformation equivalence.

In a series of recent articles I showed that, at least for small $b_2$, the second conjecture can be proved using methods from Donaldson theory. In this talk I will concentrate on minimal class VII surfaces with $b_2\leq 2$, and I will present recent results on the geometry of the corresponding moduli stacks.




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