
photo
by A. Adarve

My research interests are
mainly in Non
Commutative Geometry, Operator
algebras and index theory, with a special focus on foliations. I am also interested
in homologies of algebras associated with some
groupoids and the residue formulae for noncommutative manifolds. I have
also studied Lefschetz fixed
point formulae for foliated isometries... Here is a proceeding paper, written on the occasion of a lecture series I gave in Villa de Leyva in Colombia, with a long overview of the AtiyahSinger index theorem for beginners: Noncommutative geometry and abstract integration theory See Animated Foliation Samplers (realized by Takashi Tsuboi) 

Etats de la Recherche GNC, Metz Nov. 2007 (Lecture by A. Connes) 
Colombia 2003 (photo by A. Adarve) 
Noncommutative Geometry workshop,
Oberwolfach Sept. 2007 
Noncommutative geometry summerschool,
Portugal, 1997 
Geometry
and QFT organized by S. Paycha, S. Rosenberg, Peter Teichner and M. Varghese, MPI Bonn, June 20th26th 2010. 
The theme of the conference is
the interaction between mathematics and physics, more specifically
between noncommutative geometry in mathematics and statistical models
and quantum field theory in physics. We will celebrate Alan Carey's
60th birthday. 

EUNCG, 28 June2 July 2010 , Cardiff 
This is the 3rd Annual Meeting of the NCG network. I shall report on my joint work with A. Gorokhovsky about the superconnection proof of the local projective index theorem. 


This is a Winter School which will cover different topics in Noncommutative Geometry, and its connections with other areas of Mathematics and Physics, such as Operator Index Theory, Strings, Representations, Operator Algebras, and KTheory. 


This a one day colloquium where I was invited to give a lecture on the CheegerGromov invariant for foliations. The 2 other speakers were S. Bloch and M. Crainic. 

Noncommutative geometry workshop organized by A. Connes, J. Cuntz and M. A. Rieffel), Oberwolfach,Sept 612, 2009 
Every two years, the NCG network meets at Oberwolfach and all the relevent questions are discussed. The last workshop took place in sept. 2007. 

Spring school on Index theory, Lie groupoids and boundary value problems The title of my lecture series is ''Index theory for foliations''. It is adressed to students and young researches in the domain of non commutative geometry for foliations. 
Abstract:We shall first outline the Ktheory approach to the longitudinal index formula for foliations and explain the GRR theorem obtained using the Chern character in Haefliger cohomology. If time permits, we shall also describe a differential geometry proof of the homotopy invariance of the higher harmonic signature, recently obtained in collaboration with James Heitsch. For family reasons, I couldn't attend this school, and the course was eventually delivered by my collaborator James Heitsch. 

Programme on "Number Theory and Physics",  Special
program at the
International Erwin Schroedinger Institute (ESI) in
Vienna from March 2  April 18, 2009. 
Mehdia/GNC I: GNC et physique Ecole de printemps 
This is a spring school that I coorganized with friends in Morocco. It is intended to be the first of a series of schools that will promote the NCG research in some moroccan labs. The next school is already decided. 
Session GNC, Nov. 2007 at Metz 
With two colleagues in Metz (N. Louvet and J.L. Tu), we organized the ''Etats de la recherche de la Société Mathématique de France'' in Metz, on the theme of noncommutative geometry. We also took this opportunity to propose a colloquium at the Hotel de Ville de Metz, delivered by Alain Connes, the title was ''Un espace non commutatif engendre son propre temps. See the dvd of the colloquium . 
Application géométrique de l'analyse microlocale 
This is a conference that I coorganized with colleagues from other universities (E. Leichtnam from Paris 6, B. Monthubert from Toulouse, F. Pacard from Paris 12 and P. Piazza from Roma) in honor of Professeur R. Melrose (MIT), June 2008, CIRM. 