Programme
The scientific programme will start
on
Monday, November 4 in the afternoon and last till
Wednesday, November 6, 2013 around noon.
Conference dinner
The conference dinner will take place in the restaurant
La Lorraine,
7 place d'Armes, L1136 Luxembourg, on Tuesday 5 at 19:30pm.
A fee of 10 € will be asked to the participants at the conference registration on Monday.
Talks:

Damien Calaque (ETH Zürich)

Giovanni Felder (ETH Zürich)

Gregory Ginot (Paris 6)

Julien Grivaux (CNRS)

Stephane Guillermou (CNRS)

Dominic Joyce (Oxford)

Yakov Kremnitzer (Oxford)

Sergei Merkulov (Luxembourg)

Dmytro Shklyarov (AlbertLudwigsUniversität Freiburg )

Michel Vaquié (Toulouse)
Titles and abstracts:

Damien Calaque, "Lagrangian structures on derived mapping
stacks and classical topological field theories"
Abstract:
In this talk I will present an extension of a result of PantevToenVaquieVezzosi on
the construction of shifted symplectic structures on derived mapping stacks
(which can be viewed as an approach to the AKSZ construction that avoids problems
involving infinite dimension). The main new ingredient compare to PTVV is the presence
of boundary conditions, which are necessary if one wants to understand the work
of CattaneoFelder on the Poisson sigmamodel. I will also explain how this is
related to the project of constructing various extended Topological Field Theories
with values in an appropriate category of Lagrangian correspondences
(inspired by the work of CattaneoMnevReshetikhin).

Giovanni Felder, "Holomorphic modular forms for SL(3,Z)"
Abstract:
I will present an attempt to extend the theory of holomorphic
modular forms to the case of congruence subgroups of
SL(n,Z). I will discuss examples for n=3, related to the elliptic
gamma function. A map to automorphic forms, generalizing
the relation between classical modular forms and Maass forms
will be described.

Gregory Ginot, "Factorization algebras and applications to Enalgebras"
Abstract:
The talk will illustrate how to study the category of Enalgebras using
factorization algebras and factorization homology techniques.
In particular, we will describe the universal enveloping Enalgebra
associated to a Lie algebra, explain the notion of centralizers of
factorization algebras and its application to higher Deligne conjecture, iterated Bar construction.

Julien Grivaux, "The geometry of quantized analytic cycles"
Abstract:
In this talk, we will give an overview of the theory of quantized analytic
cycles and present some new results concerning derived intersections. Then we will explain
how to construct characteristic classes attached to them.

Stephane Guillermou, "Eliashberg's $C^0$rigidity theorem and microlocal sheaf theory"
Abstract:
Eliashberg's theorem says that the group of symplectic diffeomorphisms of a
symplectic manifold is $C^0$closed in the group of all diffeomorphisms.
A classical result of the microlocal theory of sheaves says that the
microsupport of any nonzero sheaf is an involutive subset of the cotangent
bundle.
We will explain how to deduce Eliashberg's theorem from the involutivity
theorem.

Dominic Joyce, "Categorification of DonaldsonThomas theory using perverse sheaves"
Abstract:
This is an overview of a collection of projects joint with O. BenBassat, C. Brav, V. Bussi, D. Dupont, S. Meinhardt and B. Szendroi.
Pantev, Toen, Vezzosi and Vaquie introduced the notion of kshifted symplectic structure on a derived scheme or derived stack, for all integers k, where 0shifted symplectic structures on derived schemes are just
classical algebraic symplectic structures on classical smooth schemes. They prove that derived moduli stacks of (complexes of) coherent sheaves on a CalabiYau mfold have a (2m)shifted symplectic structure. So the case k = 1 is relevant to DonaldsonThomas theory of CalabiYau 3folds.
We prove a "Darboux Theorem" for kshifted symplectic derived schemes for all k < 0. When k = 1, this says that a 1shifted symplectic derived scheme (which includes moduli schemes of simple (complexes of) coherent sheaves on a CalabiYau 3fold) is Zariski locally equivalent to the critical locus of a regular function on a smooth scheme.
Next, we define "dcritical loci" (X,s), a classical scheme X with an extra (classical) geometric structure s which records information on how X may be written locally as a critical locus. We construct a truncation
functor from 1shifted symplectic derived schemes to dcritical loci, and deduce that moduli schemes of simple (complexes of) coherent sheaves on a CalabiYau 3fold are dcritical loci.
A dcritical locus (X,s) has a "canonical bundle", which for moduli schemes is the determinant line bundle of the natural obstruction theory. An "orientation" is a choice of square root of this canonical bundle; this is
essentially the same as "orientation data" in the work of KontsevichSoibelman.
We prove that an oriented dcritical locus (X,s) carries a natural perverse sheaf P_{X,s} (also a Dmodule, and a natural mixed Hodge module), such that if (X,s) is locally modelled on Crit ( f : U > C) then P_{X,s}
is locally modelled on the perverse sheaf of vanishing cycles of f. The pointwise Euler characteristic of P_{X,s} is the Behrend function of X. For a DT moduli scheme, the graded dimension of the hypercohomology
H^*(P_{X,s}) is the corresponding DonaldsonThomas invariant. Thus, this provides a categorification of DonaldsonThomas invariants.
We also prove that an oriented dcritical locus (X,s) carries a natural motive M_{X,s}, such that if (X,s) is locally modelled on Crit ( f : U > C) then M_{X,s} is locally modelled on the motivic Milnor fibre of f.
Applied to CalabiYau 3fold moduli schemes, this is relevant to motivic DonaldsonThomas invariants a la KontsevichSoibelman.
There is quite a lot more (mostly work in progress) that I will not have time to cover in the talk, but will be happy to discuss privately, including extensions of the above from schemes to Artin stacks, applications to
Lagrangian intersections (a la BehrendFantechi) and defining "Fukaya categories" using perverse sheaves, and further categorification of DT moduli schemes / Lagrangian intersections using matrix factorization
categories.

Yakov Kremnitzer, "Analytic geometry as relative algebraic geometry"
Abstract:
I will report on joint work with Oren BenBassat on a new approach to analytic geometry.
Following the work of Deligne and ToenVaquie on geometry
relative to a symmetric monoidal category, we develop geometry relative to the category of Banach spaces.
This gives a new approach to analytic geometry in both
the Archimedean and nonArchimdean settings. Working over the real numbers this gives a new approach to differential geometry as well.

Sergei Merkulov, "An exotic automorphism of the Lie algebra of polyvector fields"
Abstract:
Using some new operads of compactified semialgebraic configuration spaces,
we show an explicit formula for a universal action of an element of
the GrothendieckTeichmueller group as a Lieinfinity automorphism
of the Lie algebra of polyvector fields on an arbitrary smooth manifold.

Dmytro Shklyarov, "On Hodge theoretic and categorical invariants of singularities"
Abstract:
The goal of the talk is to explain how various Hodge theoretic invariants (the vanishing
cohomology with its Hodge filtration, the spectrum, etc.) of an isolated critical point of
a polynomial can be recovered from the category of matrix factorizations associated with the singularity.

Michel Vaquié, "Shifted Symplectic Structures"
Abstract:
We introduce the notion of nshifted symplectic
structures, a generalization of the notion of
symplectic structures on smooth varieties and
schemes.
This notion is an important tool to study the moduli
spaces of sheaves on higher dimensional manifolds
from the point of views of homotopy theory and
deformation quantization.
(joint work with Tony Pantev, Bertrand Toen and
Gabriele Vezzosi).