Post-doctorat Research fellow of the Labex MiLyon, ENS de Lyon
email: firstname.lastname@ens-lyon.fr (Isao is my first name)
My email @warwick is no longer active.
I am mostly working on stochastic analysis and its application to mathematical physics and geometry, although I have broad interests in mathematics.
At the moment my research is primarily focused on Symanzik/Dynkin's approach to constructive quantum field theory, especially when applied to the Higgs-Yang-Mills field : the main goal is to provide a construction of the field, as well as formula for polynomial moments in its so-called string and loop observables, in term of some random variables associated to brownian paths.
This problem brings many questions in relation with other area in stochastic analysis, in connection in particular to determinants of laplace-type operator and more general partition functions. Brownian loop soup and SLE2 processes, in particular, are naturally connected to this problem.
Initially motivated by its relation to the Higgs-Yang-Mills 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 very outstanding properties.
In french, a more detailed summary of my work and research project (dated from early 2026).
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' formula, Amperean area,
Brownian motion interacting with random magnetic impurities, occupation and intersection measures.
- EQFT, Yang-Mills-Higgs field, Gaussian free field and log-correlated fields in general, Phi(4).
- Brownian loop soup, multiplicative chaoses and LQG, 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 actually in post-doc at the ENS de Lyon, supervised by Adrien Kassel. Previously I was a PDRA at the university of Warwick and at the university of Oxford.
I did my PhD in Paris (LPSM) supervised by Thierry Lévy.
I also spend some time at the universities of Luxembourg, Vienna, and Cambridge. My collaborators include Pierre Perruchaud and
Nathanaël Berestycki.