Post-doctoral Research fellow of the Labex MiLyon, based at the ENS de Lyon
email: firstname.lastname@ens-lyon.fr (Isao is my first name)
I am mostly working on stochastic analysis and its application to mathematical physics and geometry, although I have broad interests in mathematics.
My CV in French and
in English.
At the moment my research is primarily focused on Symanzik/Dynkin's approach to constructive quantum field theory, especially when applied to the Yang-Mills-Higgs field: the main goal is to provide a construction of the field, as well as formulas for polynomial moments in its so-called string and loop observables, in terms of some random variables associated to Brownian paths (these moments are roughly speaking the gauge-invariant equivalent of the correlation functions of a scalar field).
This problem raises many questions in relation with other areas in stochastic analysis, in connection in particular to determinants of Laplace-type operator and more general partition functions. Brownian loop soup and Schramm-Loewner Evolutions with parameter 2 (SLE(2)), in particular, are naturally connected to this problem.
Initially motivated by its relation to the Yang-Mills-Higgs field,
I heavily studied the winding function associated with a planar Brownian loop. Considered as a function defined on the plane, it behave as a log-correlated field with outstanding properties.
Here is a more detailed summary of my work and research project (dated from early 2026), in French.
Some detailed presentation (in English) of Symanzik's program applied to the Higgs--Yang--Mills fields will be added shortly, come back later if you are interested!
Main interests:
- Planar Brownian motion, Brownian windings, stochastic Green's formula, Amperean area,
Brownian motion interacting with random magnetic impurities, occupation and intersection measures.
- Euclidean Quantum Field Theory, Yang-Mills-Higgs field, Gaussian free field and log-correlated fields in general, Phi(4).
- Brownian loop soup, multiplicative chaoses and Liouville Quantum Gravity, loop-erased random walks and SLE.
- Stochastic approaches to index theory, analytic torsion, measures on moduli spaces, determinant of Laplacians and Dirac operators.
- Rough path theory and Young integration (in particular, Stokes' theorems and other identities of geometric nature in these framework).
- Occasionally I also worked on problems in random matrix theory, reflected processes, stable processes.
I am currently in post-doc at the ENS de Lyon, supervised by
Adrien Kassel. Previously I did a post-doc at the university of Warwick, supervised by
Aleksandar Mijatovic and a post-doc at the university of Oxford
supervised by
Jon Keating.
I did my PhD in Paris (LPSM) supervised by Thierry Lévy.
I also spend some time at the universities of Luxembourg, Vienna, and Cambridge. In October I will be visiting Pierre Perruchaud at the university of Monash.
Co-authors :
Nathanaël Berestycki.
Johannes Forkel
Aleksandar Mijatovic
Pierre Perruchaud
Andrey Pilipenko
Andrew Wade