Trag2026

Liste des Contributions

1. Horatio Boedihardjo

08/06/2026 14:00

Decay rate of logarithmic signature

It was conjectured by T. Lyons and N. Sidorova that, with the exceptions of straight lines, the logarithmic signatures of tree-reduced bounded variation paths have infinite radius of convergence. This conjecture was confirmed in the same work for certain types of paths and the general BV case remains unsolved.
In this talk, we develop a deeper...

2. Nathan Benichou

08/06/2026 15:30

Unbounded nonconvex Young differential inclusions: existence of a measurable selection of solutions

We study the differential inclusion $\text{d} z_t\in F(z_t)\text{d} x_t$, with initial condition $z_0=\xi$,
where $F$ is a nonconvex-valued multifunction, and $x$ a path of bounded $q$-variation,
for some $1\le q<2$, extending the work of Bailleul, Brault and Coutin (2020).
We obtain...

6. Łukasz Mądry

08/06/2026 16:30

Ergodicity of fractional SDEs with singular drift

In this talk I will present a result on the construction of the unique invariant measure of the singular SDE with fractional Brownian noise (fBm), equipped with a linear damping. We build up on the theory of regularisation by noise, developed in recent years by Catellier, Gubinelli, Galeati and many others, and merge it with ergodic theory...

3. Alexandre Richard

09/06/2026 09:50

Directed polymers in a singular fractional environment: well-posedness and free-energy asymptotics

Directed polymers in random environments describe paths which are subject to competition between entropy, which favours diffusion, against the energy of a random, disordered medium, which favours localisation. After a brief word on polymer models in continuous space-time media, I will turn...

4. Antoine Lejay

09/06/2026 11:15

Why trees in Runge-Kutta methods

While Runge-Kutta methods for solving ODE have been introduced around 1900, J. Butcher presented in the 1970's a set of algebraic techniques to check the order of a Runge-Kutta method.
This approach in now one of the pillars of the geometric integration theory. We give an intuitive account on why trees appear in such a problem and how transform is into an...

5. Chengcheng Ling

09/06/2026 14:00

Stroock--Varadhan martingale problem of Young stochastic differential equations

Under mild regularity assumptions, we prove that the martingale problem associated with the hybrid Young-Lyons-Itô differential equation admits a unique solution, thereby establishing probabilistic weak well-posedness. Our proof relies on analysis of the associated Kolmogorov equations, which are Young-type...

7. Dimitri Sotnikov

09/06/2026 15:30

Chasing Stationarity: Exponentially Fading Memory Signature

We introduce the exponentially fading memory (EFM) signature, a time-invariant transformation of an infinite (possibly rough) path that serves as a mean-reverting analogue of the classical path signature. We construct the EFM-signature via rough path theory, carefully adapted to accommodate improper integration from minus infinity....

8. Anton Baeza

09/06/2026 16:30

Gaussian driven Mckean-Vlasov equation

We study McKean--Vlasov equations driven by Gaussian rough noise. We exploit a regularization effect in the measure variable to transform the equation into one with a time-dependent vector field of complementary Young regularity.

The regularity gain is obtained through Gaussian integration by parts and the Duhamel formula from rough path theory,...

9. Joscha Diehl

10/06/2026 09:00

Tensor-to-Tensor Models with Fast Iterated Sum Features

We present a new class of tensor-to-tensor (in particular: image-to-image) models based on iterated sums.
Their efficient computation is inspired by recent breakthrough results in the field of permutation pattern counting.
Work in progress with R. Ibraheem, L. Schmitz and Y. Wue.

10. Aurélien Deya

10/06/2026 10:30

An SPDE model: the $\Phi_3^4$ equation for the harmonic oscillator

We will first present the physical motivations behind this model, then turn to the comparison with its "standard" counterpart, in which the harmonic oscillator (on $\mathbb{R}^3$) is replaced by the Laplacian on the torus.

The results, from joint work with Reika Fukuizumi (Tokyo) and Laurent Thomann (Nancy), include the...

11. Nicolas Moench

10/06/2026 11:30

A general paracontrolled ansatz for singular SPDE

In this talk, we will present the paracontrolled approach to singular SPDEs and discuss its main ingredients. This framework enables us to give a definition for the ill-posed non-linearities from the equation at hand, and perform a fixed point argument in some suitable space of paracontrolled distributions. We will try to genaralize these...