Monty Essid

CIMS Webpage

Research

Current

PDEs and Stochastic Analysis

As explained in my home page, I am interested in areas related to PDEs and stochastic analysis, as well as their applications in Physics and Finance.
My research topics include: deterministic/stochastic optimal control and the Hamilton-Jacobi-Bellman equations, convex optimization and duality, and optimal transport applications.
Other interests include numerical aspects of PDEs and Monte Carlo simulations.


A more comprehensive description of my research will be updated at a more convenient time as well as research reports.

Example of applications I am interested in:

  • Physics: Friction, rolling, sliding in stochastic systems, diffusions on manifolds for systems with non-holonomic constraints. White noise smoothing and asymptotics in SDEs.
  • Finance : Convex Duality techniques, Optimization, Stochastic Optimal Control, Optimal Transport and its applications in Math for Finance.
  • Other : Optimal transport applications to Machine learning and Image analysis.

Past

Anisotropic Mesh Adapting techniques

This research project part of a module conducted by Jacques-Hervé SAIAC , Pascal Frey and Frédéric Alauzet at École Centrale Paris aimed at using anisotropic mesh adapting techniques to various applications ranging from PDE solving, CFD and image compression. Most modules are open source and developped by them and I recommend visiting their websites for further information.

Topology of the one-reduced electron density matrix

This research project conducted by Jean-Michel Gillet (ECP) aimed at studying topological aspects of the one-reduced electron density matrix, a quantum physics function which is essentially the square of the wavefunction which has had all of the electron coordinates except one `integrated out'. It allows computing averages of observable quantitiies in quantum systems efficiently.
A software was developped using variational techinques and basis set expansions to visualize this matrix for any molecule.

Other projects will be updated at a more convenient time