I am a C.L.E. Moore Instructor at the Massachusetts Institute of Technology. Before that, I was a PhD student in mathematics under the supervision of Viviane Baladi. For further details, you may refer to my curriculum vitae.
Contact: mpjez [at] mit [dot] edu
I study statistical properties of hyperbolic dynamical systems by functional analytic methods. Doing so, I developed an independent interest for PDE techniques, such as microlocal analysis, in particular in the context of high regularity (real-analytic, Gevrey, ultradifferentiable,...). During my PhD thesis, I addressed the question of trace formulae for uniformly hyperbolic dynamics.
- Notes from a minicourse on resonances in hyperbolic dynamics given during the summer school "Microlocal and probabilistic methods in geometry and dynamics" in Jussieu in July 2023.
- Distribution of Ruelle resonances for real-analytic Anosov diffeomorphisms (preprint, submitted).
- Upper bound on the number of resonances for even asymptotically hyperbolic manifolds with real-analytic ends (preprint, submitted).
- Scattering rigidity for analytic metrics with Yannick Guedes Bonthonneau and Colin Guillarmou (preprint, submitted).
- Rigorous justification for the space-split sensitivity algorithm to compute linear response in Anosov systems, with Nisha Chandramoorthy, 2022, Nonlinearity 35 4357.
- Semiclassical measures for higher dimensional cat maps, with Semyon Dyatlov. Annales Henri Poincaré, online first.
- Manuscript of my PhD thesis.
- FBI Transform in Gevrey Classes and Anosov Flows, with Yannick Guedes Bonthonneau (preprint, submitted).
- Transfer operator for ultradifferentiable expanding maps of the circle, Ergodic Theory and Dynamical Systems, 41, No. 7, 2049-2068 (2021).
- Global trace formula for ultra-differentiable Anosov flows, Communications in Mathematical Physics, 385, No. 3, 1771-1834 (2021).
- Local and global trace formulae for smooth hyperbolic diffeomorphisms, J. Spectr. Theory, 10 (2020), 185-249.
- Parameter regularity of dynamical determinants of expanding maps of the circle and an application to linear response, Discrete and Continuous Dynamical Systems - Series A, 39(2):927-958, 2019.
- Réponse linéaire et points périodiques : cas analytique, master degree's thesis under the supervision of Viviane Baladi (in French).