Mathematician

Invariant measures, randomness, and the equations that carry them

I work at the meeting point of nonlinear partial differential equations and stochastic analysis. Most of my research asks a single question in different guises: what does a Hamiltonian or fluid equation preserve over long times, and what can a well-chosen measure tell us that a single trajectory cannot?

That question has taken me through invariant measures for the Benjamin–Ono and Klein–Gordon equations, almost sure global well-posedness in the energy supercritical regime, and invariant measures for the surface quasi-geostrophic and Euler equations. The method built on inviscid limits of damped and driven equations, turns out to reach problems where deterministic techniques stop.

Since taking the German Research Chair at AIMS Rwanda I have been building something alongside the research: a school focused on probabilistic methods in PDEs, within a DAAD cooperation with Bielefeld University.

Currently

PositionGerman Research Chair in Mathematics and its Applications, AIMS Rwanda, funded by the Alexander von Humboldt Foundation
Also atAnnual three-month research residency, University of Bielefeld
DirectingPDEs and Randomness, the annual summer school at AIMS Rwanda, fourth edition in December 2026
BuildingStochArena, an interactive probability and statistics platform in French, English and Pulaar
1 to 11 December 2026 · AIMS Rwanda, Kigali

PDEs and Randomness, fourth edition

Eleven days of lecture courses, working sessions and posters for graduate students and early-career researchers. Fully funded: travel, accommodation and meals. Applications close 15 September 2026.

Call for applications

Research

Publications and preprints

Partial differential equations and stochastic analysis: nonlinear Schrödinger and wave equations, supercritical equations, invariant and Gibbs measures, Euler and Navier–Stokes type equations, KPZ universality.

Preprints and submitted work

preprint Probabilistic global well-posedness for the energy supercritical Schrödinger equations on compact manifolds with S. Gueye and F. G. Longmou-Moffo arXiv:2502.08812
preprint Almost sure global well-posedness for 3D Euler and other fluid dynamics models with J. Földes
submitted Almost sure global well-posedness for the energy supercritical NLS on the unit ball of R3 with X. Yu

Published

NLS with exponential nonlinearity on compact surfaces with F. G. Longmou-Moffo · Nonlinearity 39 DOI
On properties of statistically stationary solutions to the one-dimensional Schrödinger map equation with E. Gussetti · Journal of Dynamics and Differential Equations DOI
Regularity and pathwise bounds for probabilistic solutions of PDEs Journal of Mathematical Analysis and Applications DOI
Global well-posedness of the cubic fractional NLS on the unit disc with X. Yu · Nonlinearity DOI
Invariant measures and global well-posedness for the SQG equation with J. Földes · Archive for Rational Mechanics and Analysis DOI
Global well-posedness and long-time behavior of the fractional NLS with X. Yu · Stochastics and Partial Differential Equations: Analysis and Computations 10(4), 1261–1317 DOI
Almost sure global well-posedness for the energy supercritical Schrödinger equations Journal de Mathématiques Pures et Appliquées DOI
Invariant measure and large time dynamics of the cubic Klein–Gordon equation in 3D Stochastics and Partial Differential Equations: Analysis and Computations DOI
Invariant measure and long time behavior of regular solutions of the Benjamin–Ono equation Analysis & PDE 11(8), 1841–1879 DOI
Invariant measures for Hamiltonian PDEs Doctoral thesis, Université de Cergy-Pontoise · advisors A. Shirikyan and N. Tzvetkov Mathematics Genealogy

General questions I am working on

  • Statistics of turbulence.
  • Well-posedness beyond determinism.
  • New innovative approches in the probabilistic theory of PDEs.

Activities

Schools, talks and public engagement

Events I organise or take part in. The summer school is the one I run.

1 to 11 December 2026 · AIMS Rwanda, Kigali

PDEs and Randomness, fourth edition

The annual summer school I direct at AIMS Rwanda. Eleven days of lecture courses, problem sessions and poster evenings, for master's students, doctoral students and postdocs working across probability and partial differential equations. Fully funded, applications close 15 September 2026.

Programme and call for applications

Upcoming

Sep 2026 Symposium on Systems Optimization for Sustainable Resources Utilization 22 to 24 September · AIMS Research and Innovation Centre, Kigali · invited speaker

Public engagement

Nouakchott Kinkéli-Débat at ESTIM: what do the statistics say about us? Public debate on statistical literacy.
Nouakchott Course at the Université de Nouakchott Short course delivered during a working visit
Media Television and radio on mathematics in African languages Including interviews on mathematics education in African languages

Teaching

Courses and written material

Courses

AIMS Graduate courses at AIMS Rwanda Probability, stochastic analysis and partial differential equations
Course Probabilistic Methods in PDEs A lecture course for a mixed audience

Interactive

Platform

StochArena

An interactive probability and statistics platform in French, English and Pulaar. Experiments students run rather than read about... stocharena.com

Curriculum vitae

Positions and education

Positions

Current German Research Chair in Mathematics and its Applications Humboldt African Institute for Mathematical Sciences, Rwanda · funded by the Alexander von Humboldt Foundation
Annual Research residency University of Bielefeld · three months each year
2022–23 Johns Hopkins University Department of Mathematics
2021–22 Research Associate, Imperial College London In the group of Prof. Martin Hairer
2018–21 Research Associate, University of Virginia
2017–18 Teaching and research assistant, Université de Cergy-Pontoise

Education

2017 Doctorate in Mathematics, Université de Cergy-Pontoise Thesis: Invariant measures for Hamiltonian PDEs · advisors Armen Shirikyan and Nikolay Tzvetkov Mathematics Genealogy