Workshop at ENS Paris

Date and duration:
November 14-15, 2011

Topic: All topics of the ANR SÉDIGA program

Where?: ENS Paris,
45 rue d'Ulm, salle W

Organizers &
Contacts:

Program:

Monday, November 14

14h30-15h30 Thomas
Reichelt (FSMP, ENS Paris): Laurent polynomials,
hypergeometric systems and mirror symmetry

Abstract: In this
talk I will explain a close relationship between the
Gauss-Manin systems of families of Laurent polynomials and the
A-hypergeometric systems of Gelfand, Kapranov and Zelevinsky.
As an application I will discuss the computation of the mirror
Landau-Ginzburg model of a smooth, toric, Fano variety.

16h-17h Carlos
Simpson (CNRS, Nice): Functoriality in nonabelian Hodge theory

Abstract: The goal
of this work in progress with R. Donagi and T. Pantev, is to
try to understand the parabolic structure of the higher direct
image Higgs bundle in terms of the parabolic structure on a
Higgs bundle on the domain variety of a map.

17h30-18h30 Hélène
Esnault (Essen and ENS Paris): On a variant in equal
characteristic p
of the conjecture on p-curvatures

Abstract: This is
a joint work with Adrian Langer (pdf)

This conjecture is false as such (the corresponding one in
equal characteristic zero is true, after Yves André).
We correct the formulation and we show a part of what can be
supposed to hold.

19h45 SÉDIGA Dinner

Tuesday,
November 15

9h-10h Christian
Sevenheck (Mannheim): Gauß-Manin systems and free divisors

Abstract: I will
present some results (a joint work with D. Mond and I. de
Gregorio) concerning Gauß-Manin systems of hyperplane
sections of Milnor fibers of some non isolated singularities,
namely, the linearly free divisors. These singularities appear
in the theory of representations of quivers. Our construction
is a generalization of the mirror of the quantum cohomology of
the projective space. If time permits, I will also speak of
the Bernstein polynomial of these singularities, and of some
very speculative ideas on the mirror objects of the linearly
free divisors.

10h30-11h30 Michel
Granger (Angers): Partial
normalizations of Coxeter arrangements and their
discriminants

Abstract: In a
joint work with D. Mond and M. Schultze, we study a partial
normalization of a Coxeter arrangement and its discriminant.
The ring structures occurring come from the Frobenius manifold
structure on space of orbits which contains the discriminant
and from a lifting (without a unit) to the space of the
arrangement. We also give another description by using a
duality on fractional maximal Cohen-Macaulay ideals, and this
produces a differential condition of order 3 on the Coxeter
invariants. These normalizations also allow us to construct
new free divisors by a kind of adjunction.

12h-13h Antoine
Douai (LJD, Nice): Mirror
symmetry and quantum differential systems : example(s) and
application(s)

Abstract: We
describe an aspect of mirror symmetry (correspondence between
the A side (quantum cohomology) and the B side
(singularities)) by using bundles with meromorphic
connections. The starting idea is that the latter may be
computed on the B side (in some cases), by using "elementary"
methods. This correspondence can be used to define rational
structures on the A side, and this generalizes a well-known
method. In this context, the conformal solutions of Dubrovin
play a central role.

13h-14h30 Lunch

14h30-15h30 Phil
Boalch (CNRS, ENS Paris): Fission varieties

Abstract: I'll
recall the quasi-Hamiltonian approach to moduli spaces of flat
connections on Riemann surfaces, as a finite dimensional
algebraic version of operations with loop groups, such as
fusion. Recently, whilst extending this approach to
meromorphic connections, a new operation arose, which we will
call fission. This
operation enables the construction of many new algebraic
symplectic manifolds, going beyond those we were trying to
construct, and suggests some conjectures about the irregular
analogue of the Deligne-Simpson problem.

15h45-16h45 Alexandru
Dimca (LJD, Nice): Hodge
theory for projective hypersurfaces and applications

Abstract: We will
discuss recent results concerning the relation between the
Hodge filtration and the filtration by the order of the pole
on the cohomology of the complement of a complex projective
hypersurface D.
Applications concern bounds on the degree of syzygies between
the partial derivatives of the defining equation for D.

17h-18h Viktoria
Heu (Strasbourg): Rank
two connections on genus two curves

Abstract: We will
present the construction of a moduli space of suitable rank
two vector bundles on genus two curves, which allow to study
unstability phenomena along analytic families of such bundles.
This result, which is a joint work in progress with Frank
Loray, relies on a symmetry, discovered by William Goldman, of
rank two connections, which is specific to the genus two case.