I am an assistant professor at Université Lyon 1 since September 2011, among the Probability and Mathematical Physics group.
Office: Braconnier 227
I coorganize the following conference Probably on Random Matrices.
Main Research Interests
Free Probability theory, especially the study of free stochastic differential equations, free entropy, free transport (conjecturally optimal).
Applications of free probability to von Neumann algebras.
Algebraic quantum field theory.
Publications and preprints
Most of my articles can be found on Arxiv.
Links to published versions or preprints can be found bellow.
Continuous model theory and logic .
- A non-commutative Path Space approach to stationary free Stochastic Differential Equations Arxiv:1006.4351
- A Free Stochastic Partial Differential Equation. Ann. Inst. H. Poincaré Probab. Statist.
Volume 50, Number 4 (2014), 1404-1455. (Slightly more general results with a worse exposition in the second older arxiv version Arxiv:1008.4742v2 )
- (with Philippe Biane) Concavification of free entropy. Advances in Mathematics Volume 234, 15 February 2013, Pages 667–696
- (with Ken Dykema and Kunal Mukherjee) The simplex of tracial quantum symmetric states Studia Mathematica 225 (2014), 203-218.
Time Reversal of free diffusions I : Reversed Brownian motion, Reversed SDE and first order regularity of conjugate variables Arxiv:1402.4774
Non-commutative Analytic functions relative to a covariance map : I. Generalized Haagerup products and analytic relations Arxiv:1503.05515
A Laplace Principle for Hermitian Brownian Motion and Free Entropy Arxiv:1604.06420
(with Alice Guionnet and Dima Shlyakhtenko) Free transport for convex potentials Arxiv:1701.00132
Applications to von Neumann algebras, Subfactors.
- Continuous model theories for von Neumann algebras Arxiv:1508.03202
- (with Marie Kerjean) Models of Linear Logic based on the Schwartz $\varepsilon$-product Arxiv:1712.07344
Functional Analysis related to Algebraic quantum field theory.
- A Note about proving non-Γ under a finite non-microstates free Fisher information Assumption. Journal of Functional Analysis. Volume 258, Issue 11, 1 June 2010, Pages 3662–3674
- (with Adrian Ioana) Unbounded derivations, free dilations and indecomposability results for II_1 factors Arxiv:1212.6425 (To appear in Trans. Amer. Math. Soc. )
- (with Stephen Curran and Dimitri Shlyakhtenko) Free analysis and planar algebras. Proceedings of the 2014 Maui and 2015 Qinhuangdao conferences in honour of Vaughan F.R. Jones’ 60th birthday p 115
- (with Christian Brouder) Functional properties of Hörmander's space of distributions having a specified wavefront set.
Communications in Mathematical Physics December 2014, Volume 332, Issue 3, pp 1345-1380
- Functional properties of Generalized Hörmander spaces of distributions I : Duality theory, completions and bornologifications
- Functional properties of Generalized Hörmander spaces of distributions II : Multilinear maps and applications to spaces of functionals with wave front set conditions
- (with Alexander I. Bufetov and Yanqi Qiu ) Linear rigidity of stationary stochastic processes. Arxiv:1507.00670