Since 09/2021, I am a Maitre de conference at Paris-Saclay University. Before this
I was a postdoc at Muenster university from 09/2019 to 08/2021
I was a PhD student of G. Skandalis at Paris Diderot university. I defended my thesis on 04/10/2018.
Publications
Chern Simons invariants in KK theory. Published in Journal of Functional Analysis (2019).
Summary : We define a universal element in equivariant KK theory whose pullback by the classifying map of a unitary flat vector bundle is the Chern Simons invariant.
On the deformation groupoid of the inhomogeneous pseudo-differential Calculus. Published in Bulletin of London mathematical society (2020).
Summary : We give a simple construction using an iterated deformation to the normal cone construction of the deformation groupoid of Carnot manifolds defined by van Erp and Yuncken and independently by Choi and Ponge.
Witten deformation using Lie groupoids. Published in Advances in Mathematics (2022).
Summary : We give a global point of view to Witten deformation using deformation to the normal cone construction. We show that this point of view extends effortlessly to any regular foliation. As a corollary, we obtain a new proof of Connes-Fack Morse inequalities with slightly weaker hypothesis.
The convolution algebra of Schwarz kernels on a singular foliation, with I. Androulidakis and R. Yuncken. Published in Journal of Operator Theory (2019)
Summary : We define an algebra of distributions on the holonomy groupoid of singular foliations which generalise the algebra of distributions on the holonomy groupoid of a regular foliation defined by Lescure, Manchon and Vassout here
Index theorem for inhomogeneous hypoelliptic differential operators. Published in Muenster journal of mathematics (2022).
Summary : We prove an index formula for hypoelliptic differential operators on Carnot manifolds.
A blow-up groupoid for singular foliations. Submitted.
Summary : We give a topological construction to resolve singularities of an arbitrary singular foliation.
A pseudodifferential calculus for maximally hypoelliptic operators and the Helffer-Nourrigat conjecture, with I. Androulidakis and R. Yuncken. Submitted.
Summary : We prove a conjecture of Helffer and Nourrigat (1979 C.R.A.S) on the equivalence of maximally hypoellipticity of a differential operator D and the injectivity of the principal part of D under some representations of nilpotent Lie groups.
Summary : We give an index formula for the class of all maximally hypoelliptic operators (essentially any differential operator on any compact manifold for which the analytic index is finite and agrees with a Fredholm index for some bounded extension of the operator). This generalizes our work in 5. The approach used here is different and is based on our blowup construction of singular foliations in 6. The approach is also much simpler and more general which allows us to easily give new concrete index computations.
Higher order derivations on C*-algebras and applications to smooth functional calculus and Schwartz functions on the tangent groupoid. Accepted for publication in JFA (2024)
Summary : We prove that the algebra of Schwartz functions on Connes's tangent groupoid is closed under smooth functional calculus.
Tangent groupoid and tangent cones in sub-Riemannian geometry. Accepted for publication in Duke Mathematical Journal (2024)
Summary : We generalise a theorem on Bellaiche on the tangent cones in sub-Riemannian geometry by showing that there are many more tangent cones than the ones constructed by Bellaiche.
Talks
Here is a pdf file with a list of my talks. If a talk has a beamer file which I kept, then I added a link to the beamer file. The list is missing some talks from before 2022.
CV
My CV can be found here. (last updated 01/2023)
Contact
Email: omar.mohsen (at) universite-paris-saclay.fr
Telephone number: (+33) 7 81 32 99 93
Laboratoire de Mathématiques d Orsay
Topologie et Dynamique
Bureau: 2L22 Bâtiment: 307
Campus: Orsay - rue Michel Magat
91400 Orsay
Last Update 03/2024