CONFERENCES - SEMINARS
- Conference Noncommutativity and Physics 2012, May
2012, Bayrischzell .
- Isaac Newton Institute for Mathematical Sciences conference on Noncommutative Geometry, Avril 2012,
- Conference "Quantum spacetime : from discreteness to continuum", March 2011, Orsay.
- Workshop "The Physics of the Spectral action", December 2009, IHES Bure-sur-Yvette.
- Workshop on Noncommutative Geometry : Topics in mathematics and mathematical physics, November 2009, Orsay.
- 12th Marcel Grossman Meeting, July 2009, Paris.
- 17th International Colloquium on Integrable Systems and Quantum Symmetries, June 2008, Prague.
- Conference de Physique Theorique, Cycle du cinquantenaire de l'IHES,
IHES, Bures-sur-Yvette, June 2008.
- International workshop on "Differential Geometry, Noncommutative
Geometry, Homology and fundamental interactions", Orsay, April 2008.
- 4th Vienna Central European Seminar on Particle Physics and Quantum Field Theory, "Commutative
and Noncommutative Quantum Fields", Vienna, December 2007.
- ESF Workshop on Noncommutative Quantum Field Theory, Vienna, November 2007.
- Conference on Noncommutative Geometry and Physics, Orsay, April 2007.
- School on Noncommutative Geometry, Field Theories and Quantum Gravity, Oran, April 2007.
- Workshop on "Renormalization", Max Planck Institute fur Mathematik, Bonn, December 2006.
- Conference on "Noncommutative Geometry and Physics : Structure of
Space and Time", Isaac Newton Institute for Mathematical Sciences, Cambridge, September 2006.
- Workshop on "Quantum Field, Periods and Polylogarithms, IHES
Bure-sur-Yvette, June 2006.
- Workshop on "The Rigorous Renormalisation Group", Mathematisches
Forschunginstitut Oberwolfach, April 2006.
- Conference on Higher Dimensional Quantum Hall Effect, Chern-Simons
Theory and Non-Commutative Geometry in Condensed Matter Physics and Field Theory, Trieste, March 2005.
- School on Quantum Phase Transitions and Non-Equilibrium Phenomena
in Cold Atomic Gases, ICTP Trieste, July 2005.
- Conference of Societe Francaise de Physique and Belgian Physical
Society, Lille, August 2005.
SOME RECENT LECTURES, TALKS AND SEMINARS
- Metric and differential aspects of Moyal spaces.
This is a seminar I gave in the Mathematic Laboratory, University of Metz, LMAM, in April 2010. I focus on metric and differential aspects of the noncommutative
geometry of the Moyal plane described by a non unital spectral triple built from the (Frechet) algebra of the Schwartz functions on R&sub2 endowed with the Moyal product.
This provides an example of locally compact quantum (noncommutative) space. An explicit formula for the Connes spectral distance
between a specific class of pure states can be proven. The corresponding properties are discussed together with the implications
of the existence of states at infinite distance. Besides, some recent results obtained within noncommutative gauge theories on Moyal space, a class of model pertaining to Mathematical
Physics are presented. These are mainly based on the use of various derivation-based fifferential calculi.
- Spectral distance on the Moyal plane.
This is a talk I gave at the recurrent S&ecute;minaire de Physique Mathématique of the Institut Camille Jordan, University of
Lyon I and in a somehow similar way at the Mathematic laboratory of the University of Clermont in March 2010. There are some more
technical details in the last one (The corresponding slides are here)
- Spectral distance: Results for the Moyal plane and noncommutative Torus.
One studies the Connes's spectral distance for noncommutative Moyal planes described by a non compact spectral triple
recently proposed as a possible noncommutative analog of non compact Riemannian spin manifold. An explicit
formula for the distance between any two elements of a particular class of pure states is determined. The corresponding result is discussed. The
existence of pure states at infinite distance signals that the topology of the spectral distance on the space of states is not the weak * topology. The
case of the noncommutative torus is also considered and a formula for the spectral distance between some states is also obtained.
- Derivation algebras and noncommutative gauge theories.
Relevant derivation-based differential calculi for
the noncommutative gauge theories on Moyal spaces are presented. The
vacuum configurations for the
so called noncommutative induced gauge theory on Moyal space are
presented in d=2 and d=4 and discussed. The UV/IR mixing problem
occuring within the noncommutative Yang-Mills-Higgs
models on 4-d Moyal space is presented.
- Noncommutative Yang-Mills-Higgs models on Moyal spaces .
This talk is principaly writen for physicists. The
content is similar to the one of the next talk. However, a bit more
details concerning the computation in a covariant
Feyman-type gauge of the 1-loop diagrams contributing to the vacuum
polarisation tensor for 4-d gauge models have been indicated.
- Recent results in gauge theory on noncommutative Moyal space.
Derivations of a noncommutative algebra can be used to
construct differential calculi,
the so-called derivation-based differential calculi. We apply this
framework to (a unitalized version of)
the Moyal algebra M. We show that the differential calculus, generated
by the maximal
subalgebra of the derivation algebra of M that can be related to
gives rise to a natural construction of Yang-Mills-Higgs models on M and
a natural interpretion of the covariant coordinates as Higgs fields.
The corresponding UV/IR mixing problem of the resulting Yang-Mills-Higgs
models in 4-D is discussed. Finally, the vacuum
problem of the so-called induced gauge theory on Moyal space is also
discussed. As a simpler illustration, vacuum configurations are
determined within noncommutative
scalar models with harmonic term and a noncommutative analog of the
Goldstone mechanism is presented.
- Lectures on Recent advances in Noncommutative Field Theories
on Moyal spaces.
These slides are writen for physicists. Noncommutative
field theories on Moyal spaces can be conveniently handled
within a framework of noncommutative geometry. This latter is the
derivation-based differential calculus. The corresponding basics
reviewed, paying attention to the case of gauge theories. The general
scheme is applied to the version of the Moyal algebra used in the
physics litterature on noncommutative field theories. Consider the
*-algebra built from
the set of Schwartz functions endowed with the associative Moyal
product. Then, the Moyal algebra that is used is simply the
corresponding multiplier algebra. Some renormalisable matter
field theories are briefly reviewed. The construction of renormalisable
gauge theories on these noncommutative Moyal spaces is also considered
- Anyonic Excitations in Fast Rotating Bose Gases.
The role of anyonic excitations in fast rotating
harmonically trapped Bose gases in a fractional Quantum Hall State is
examined. Standard Chern-Simons anyons as well
as "non standard" anyons obtained from a statistical interaction having
Maxwell-Chern-Simons dynamics and suitable non minimal coupling to
matter are considered. Their respective ability
to stabilize attractive Bose gases under fast rotation in the
thermodynamical limit is studied. Stability can be obtained for standard
anyons while for non standard anyons, stability
requires that the range of the corresponding statistical interaction
does not exceed the typical wavelength for the atoms.
- Geometrical and
Algebraic Structures in Quantum Hall Systems.
I review the main features of a mathematical framework
encompassing some of the salient quantum mechanical and geometrical
aspects of Hall systems
with finite size and general boundary conditions. Geometrical as well as
algebraic structures controlling possibly the integral or fractional
of the Hall conductivity are discussed.