## Introduction:

Hello! I am Hugo Vanneuville, I am a researcher in math. Since January 2021, I am a CNRS researcher at

Institut Fourier (Université Grenoble Alpes) in the

probability team. Before this, I have completed a PhD at

Institut Camille Jordan (Université Lyon 1) under the direction of

Christophe Garban and I have been a post-doctoral resarcher at the

math department of ETH Zürich under the direction of

Vincent Tassion.

I am mainly interested in the study of phase transition and noise sensitivity phenomenons in percolation models. You can find more information below.

## Research interests:

I am interested in phase transition and noise sensitivity phenomenons in percolation models and in the universality properties of these models (in 2D in most of my works). In percolation theory, one studies the connectivity properties of random sets (such as a random subset of edges of a given lattice, or level sets of a random function). When the density of the random set reaches some critical value, fractal structures appear; they are the sign of the emergence of interactions at all scales.

More specifically, the following three questions are guiding my research (among others):

Can we find new ways of formalising the fact that a threshold effect appears if the event that we study "depends little on every given coordinate"?
How can we show noise sensitivity properties without using any spectral tool?
Can we prove universality properties by using noise sensitivity?
(See also

here for an interview done by INSMI when I was recruited, in which I describe my field of research - in French).

Figures: Percolation on a random tiling: each face is colored black with probability p=0.4, 0.5 and 0.6 respectively. In red: the points connected to the left side by a black path. There is a transition at p=0.5.
Research papers:
### About the phase transition in Bernoulli percolation:

*Exponential decay of the volume for Bernoulli percolation: a proof via stochastic comparison*
(preprint)
### New approaches to noise sensitivity:

*Noise sensitivity of percolation via differential inequalities*
with Vincent Tassion
(Proceedings of the London Mathematical Society, 2023)
### Random nodal lines:

*Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension d >= 3*
with Hugo Duminil-Copin, Alejandro Rivera and Pierre-François Rodriguez
(Annals of Probability, 2023 ; the published version contains one error, see the erratum. This error has been corrected in the arXiv version.)
*The phase transition for planar Gaussian percolation models without FKG*
with Stephen Muirhead and Alejandro Rivera, and with an appendix written by Laurin Köhler-Schindler
(Annals of Probability, 2023)
*Bargmann-Fock percolation is noise sensitive*
with Christophe Garban
(Electronic Journal of Probability, 2020)
*The sharp phase transition for level set percolation of smooth planar Gaussian fields*
with Stephen Muirhead
(Annales de l'Institut Henri Poincaré, prob. et stat., 2020)
*The critical threshold for Bargmann-Fock percolation*
with Alejandro Rivera
(Annales Henri Lebesgue, 2020)
*Quasi-independence for nodal lines*
with Alejandro Rivera
(Annales de l'Institut Henri Poincaré, prob. et stat., 2019)
### Voronoi percolation, noise sensitivity and dynamics:

*The annealed spectral sample of Voronoi percolation*
(Annals of Probability, 2021)
*Quantitative quenched Voronoi percolation and applications*
(Annales de l'Institut Fourier, to appear)
*Annealed scaling relations for Voronoi percolation*
(Electronic Journal of Probability, 2019)
*Exceptional times for percolation under exclusion dynamics*
with Christophe Garban
(Annales scientifiques de l'École Normale Supérieure, 2019)
### Other writings (not for publication):

*Sharpness of Bernoulli percolation via couplings*
*Overview and concentration results for nodal lines*
(introductory text for the reading group on random nodal lines organized at Zürich in 2019)
*Percolation in the plane: dynamics, random tilings and nodal lines*
(PhD thesis under the direction of Christophe Garban -- the introduction is written in French and the chapters are written in English)
Slides
Small erratum
### List of my co-authors:

Hugo Duminil-Copin,

Christophe Garban, Laurin Köhler-Schindler,

Stephen Muirhead, Alejandro Rivera,

Pierre-François Rodriguez,

Vincent Tassion
## Teaching:

I taught at Université Lyon 1 during my PhD thesis. At Université Grenoble Alpes, I taught the course "Random models on lattices" with

Loren Coquille during the first semester of the year 2023-2024. You can find the course summary

here. During the second semester of the years 2021-2022, 2022-2023 and 2023-2024, I taught with Agnès Coquio the M1 course "Markov processes".

## Diffusion (in French):

J'ai fait un exposé lors du "Barcamp" organisé par les bibliothécaires de Lyon 1 en mai 2018. Vous pouvez trouver la vidéo

ici.