Omar Mohsen

activity

20222026

collaborators

4 papers

math.DG2026

The Lie algebra generated by gradient vector fields

Bettina Kazandjian, Omar Mohsen, Eugenio Pozzoli

Let $M$ be a smooth compact manifold, and $g$ a smooth non-degenerate symmetric bilinear form on $T M$ . We prove that every smooth vector field can be written as a finite linear com…

math.SG2026

Symplectic algebroids, groupoid Toeplitz operators and deformation quantization

Clément Cren, Jean-Marie Lescure, Omar Mohsen

We use Toeplitz operators to define a star-product on Poisson manifolds whose Poisson structure is induced by a symplectic Lie algebroid. The Toeplitz operators we consider are def…

math.AP2023

A groupoid approach to the Wodzicki residue and the Kontsevich-Vishik trace

Omar Mohsen

Building on the work of Debord and Skandalis, van Erp and Yuncken introduced a groupoid approach to pseudo-differential operators which has various advantages over the classical ap…

math.DG2022

Tangent groupoid and tangent cones in sub-Riemannian geometry

Omar Mohsen

Let $X_{1}, \dots, X_{m}$ be vector fields satisfying Hörmander's Lie bracket generating condition on a smooth manifold $M$ . We generalise Connes's tangent groupoid, by constructing a c…