Programme
The scientific programme will start
on
Monday, December 10 in the afternoon and last till
Wednesday, December 12, 2012 around noon.
A detailed schedule is available here.
Evening reception
On
Monday, December 10, 2012 subsequent to the last talk there will be a
reception outside the lecture room (Salle Paul Feidert).
Conference dinner
The conference dinner is on
Tuesday, December 11, 2012 at 20h00
.
It will take place in the restaurant
La Lorraine, 7 place d'Armes, L1136 Luxembourg.
Talks:

Anton ALEKSEEV, "The Duflo Isomorphism Theorem: Hard or Soft?"

Jørgen Ellegaard ANDERSEN, "A perturbative version of the WittenReshetikhinTuraev TQFT"

Pierre BIELIAVSKY, "Noncommutative surfaces"

Miroslav ENGLIS, "Quantization, deformation and orthogonal polynomials"

Johannes HUEBSCHMANN, "A step towards Lie's dream"

Ryoichi KOBAYASHI, "Hamiltonian Volume Minimizing Property of Maximal Torus Orbits in the Complex Projective Spaces"

George MARINESCU, "Equidistribution of zerodivisors of random holomorphic sections"

Ryszard NEST, "On quantization Poisson actions"

Ilse PAGE, "Intercultural Approach to a Mathematician"

Pierre Schapira, "Microlocal Euler Class"

Peter SCHUPP, "Noncommutative nonassociative nongeometry"

Armen SERGEEV, "Magnetic Bloch theory and noncommutative
geometry"

Oleg SHEINMAN, "Almost graded Lie algebras and Riemann surfaces"

Harald UPMEIER, "Geometric Quantization and Asymptotic Expansions on Symmetric Spaces"

Rainer WEISSAUER, "Galois theory revisited"

Ping XU, "Weyl Quantization and Courant algebroids"
Titles and abstracts (pdffile):

Anton ALEKSEEV, "The Duflo Isomorphism Theorem: Hard or Soft?"
Abstract:
This talk is about the Duflo isomorphism and the KashiwaraVergne problem.

Jørgen Ellegaard ANDERSEN, "A perturbative version of the WittenReshetikhinTuraev TQFT"
Abstract:
In this talk we will review the geometric approach to the WittenReshetikhinTuraev TQFT. This will, via Toeplitz operator theory on moduli spaces of flat connections, lead us to a perturbative version of this TQFT, which has interesting relations to a number of conjectures concerning this TQFT, including the so called AJconjecture.

Pierre BIELIAVSKY, "Noncommutative surfaces"
Abstract:
TBA.

Miroslav ENGLIS, "Quantization, deformation and orthogonal polynomials"
Abstract:
From the beginning, mathematical foundations of quantum mechanics
have traditionally involved a lot of operator theory, with geometry,
groups and their representations, and other themes thrown in not
long afterwards. With the advent of deformation quantization,
cohomology of algebras and related disciplines have also entered.
In this talk, we first overview some topics in quantization which
draw heavily on complex analysis and microlocal techniques,
and then present some recent developments in the latter which in
turn were inspired by the applications in quantization.
(Joint work with S.Twareque Ali, Concordia University, Montreal.)

Johannes HUEBSCHMANN, "A step towards Lie's dream"
Abstract:
The origins of Lie theory are well known: Galois theory had clarified the relationship between
the solutions of polynomial equations and their symmetries. Lie had attended lectures by Sylow on
Galois theory and came up with the idea to develop a similar theory for differential equations and
their symmetries which he and coworkers then successfully built. At a certain stage, they noticed
that "transformations groups" with finitedimensional Lie algebra was a very tractable area. This
resulted in a brilliant and complete theory, that of Lie groups, but the connection with the origins
gets somewhat lost.
The idea of a Galois theory for dfferential equations prompted as well what has come to be
known as differential Galois theory. We will present a general approach that encompasses ordinary
Galois extensions (of commutative rings), differential Galois theory, and principal bundles
(in differential geometry and algebraic geometry). The new notion that we introduce for that purpose is that
of principal comorphism of LieRinehart algebras.

Ryoichi KOBAYASHI, "Hamiltonian Volume Minimizing Property of Maximal Torus Orbits in the Complex Projective Spaces"
Abstract:
We will prove that any U(1)^{n}orbit in P^{n}
is volume minimizing under any Hamiltonian deformation.
The idea of the proof is the following:
(1) We extend a given U(1)^{n}orbit to the moment torus fibration
{T_{t}} and consider its Hamiltonian deformation {φ(T_{t})}
where φ is a Hamiltonian diffeomorphism of P^{n}. Then,
(2) We compare a given U(1)^{n}orbit and its Hamiltonian deformation
by looking at the large kasymptotic behavior of the sequence of
projective embeddings defined, for each k, by the basis
of H^{0}(P^{n},\mathcal O(k)) obtained by the BorthwickPaulUribe
semiclassical approximation of the \mathcal O(k)BohrSommerfeld
tori of the Lagrangian torus fibrations {T_{t}} and its Hamiltonian
deformation {φ(T_{t})}.

George MARINESCU, "Equidistribution of zerodivisors of random holomorphic sections"
Abstract:
Random polynomials and more generally holomorphic sections are
a model for eigenfunctions of quantum chaotic maps. We discuss
equidistribution results for zerodivisors of high tensor powers of a
quantum line bundle.

Ryszard NEST, "On quantization of Hamiltonian actions"
Abstract:
TBA

Ilse PAGE, "Intercultural Approach to a Mathematician"
Abstract:
Living with a Mathematician for more than 30 years sometimes is a special challenge besides the fact, that he is a man. Therefore, it seems to be
worthwhile to have a closer look on what is so specific in Mathematicianâ€™s
behaviour and its impact on daily life. In order to have a scientif basis, this
talk will refer to the 3 cultural dimensions, E.T. Hall formed in 1990 in order
to understand cultural differences.

Pierre SCHAPIRA, "Microlocal Euler Class"
Abstract:
TBA

Peter SCHUPP, "Noncommutative nonassociative nongeometry"
Abstract:
Flux compactifications are useful to relate string theory to observable
phenomena and lead to mathematical structures that generalize the usual
notions of geometry. We analyze these nongeometric structures in the
context of AKSZ Courant sigma models using methods of deformation
quantization and identify a dynamical noncommutative nonassociative star
product.

Armen SERGEEV, "Magnetic Bloch theory and noncommutative
geometry"
Abstract:
In our talk we shall give an interpretation of magnetic Bloch theory in terms of noncommutative geometry. In other words, we present a “vocabulary” which allows
to reformulate basic properties of magnetic Schrödinger operator in terms of C*algebras. There was a number of papers devoted to this subject, in our presentation
we follow mainly an approach proposed by Mikhail Shubin.
As an application of this version of Bloch theory we shall give an interpretation
of quantum Hall effect in terms of noncommutative geometry.

Oleg SHEINMAN, "Almost graded Lie algebras and Riemann surfaces"
Abstract:
A boom of the 80's in applications of infinitedimensional Lie algebras and
Riemann surfaces in theoretical physics has motivated the necessity of a
closer relation between these two disciplines. This was the purpose
of introducing in 1987 the analogs of the Virasoro and KacMoody
algebras related to Riemann surfaces with marked points, called
KricheverNovikov algebras. These are Lie algebras of meromorphic
objects (functions, vector fields, currents) defined on a Riemann
surface of a finite nonnegative genus, and
holomorphic outside the marked points. A crucial structure to be
adjusted was the graded structure which had been replaced by an
almostgrading, without sacrificing the functionality. The idea of
almostgrading is due to Krichever and Novikov who have incarnated it in
the case of an arbitrary Riemann surface with two marked points. It was
a nontrivial step to generalize the almost graded structure to the case
of several marked points. The first idea (1990) and full description are
due to Schlichenmaier (see also Sadov, 1991, for a particular case).
There are quite a number other significant works due to Schlichenmaier
in the theory and applications of almostgraded infinitedimensional Lie algebras, such
as highgenera Sugawara construction and KnizhnikZamolodchikov equations, basic uniqueness results in
classification of the central extensions of KricheverNovikov and Lax
operator algebras, nonrigidity results in the deformation theory of
KacMoody and Virasoro algebras.
In my talk I will try to give at least a brief outline of some of the
above listed.

Harald UPMEIER, "Geometric Quantization and Asymptotic Expansions on Symmetric Spaces"
Abstract:
Hermitian symmetric spaces M=G/K , of compact or noncompact type, are
Kähler manifolds with a transitive action of a semisimple Lie group G.
There exist various Ginvariant quantization procedures such as the
BerezinToeplitz calculus or the Weyl calculus. In joint work with M.
Englis, Prague, we found the complete asymptotic expansion of the Moyal
type starproducts for the BerezinToeplitz quantization, both for the
compact type (also studied by Bordemann, Meinrenken and Schlichenmaier)
and for the noncompact type. The primary tool is the PeterWeyl
decomposition of the reproducing Bergman kernel into irreducible Ktypes
labelled by partitions of length
r = rank(M). A similar expansion holds for the Berezin transform (and
its inverse).
For real nonhermitian symmetric spaces, it is possible to define a
deformation of "states"( instead of "observables")
which has also an asymptotic expansion into irreducible Ktypes. This
approach generalizes the wellknown SegalBargmann transform to the
setting of curved manifolds.

Rainer WEISSAUER, "Galois theory revisited"
Abstract:
We consider some new kind of Galois
groups naturally attached to coverings of
Riemann surfaces or more generally of complex
smooth projective varieties. These groups turn out to
a mixture of both the classical discrete finite Galois
groups and certain nonclassical algebraic reductive groups.

Ping XU, "Weyl Quantization and Courant algebroids"
Abstract:
Weyl quantization is a classical result which associates a differential
operator on R^{n} to every polynomial on R^{2n}.
We will present a Weyl quantization formula for symplectic Nmanifolds
of degree 2. Applications to Courant algebroids will be discussed.