**How does the geodesic structure of a random geometry model react when the environment is disturbed a little?**

Hello! This is the webpage of a 3-day **conference about Percolation and First Passage Percolation (FPP), that will take place from Wednesday 31 May 2023 (morning) to Friday 2 June 2023 (noon) in Grenoble.** This conference is organized by Institut Fourier (Université Grenoble Alpes).

**Registrations were open from March 29 to April 27. Please send an email to hugo.vanneuville [at] univ-grenoble-alpes [dot] fr if you would like to register but the date has passed.**

**The (almost final) planning is available **(see the button on the left side of this page).

During these three days, we will focus on the general theory of percolation and first passage percolation, with **a zoom on the notions of superconcentration and chaos in FPP** (and beyond). See below for the definition of FPP and chaos. Participants will present their own work, work from other researchers, or open questions. Without rushing! The aim is to take a step back together.

**(1) **What do FPP and chaos mean? The general question of this conference is the following: "In a model of random geometry, how does the geodesic structure react when the environment is disturbed a little?" Let us now define more precisely the objects that we will study. FPP is defined as follows: consider a graph, and associate random i.i.d. weights to the edges. Then, define a random distance between two vertices x and y as follows: This is the smallest weight of a path between x and y. Let us now define chaos for FPP. Consider a FPP model (on Z^d, say) and let g be the geodesic between 0 and n e_1. Moreover, resample a fixed small proporition of the weights and let g' denote the new geodesic. Then chaos means that the size of the intersection of g and g' is typically much less than n.

**(2)** About the papers that we will study: There will essentially be two different kinds of talks / discussions during this conference:
- A few talks on various topics related to percolation and/or FPP;

- A few talks / discussions / open problem sessions in which we learn "superconcentration and chaos theory for FPP" together. In particular, there will very likely be talks about the following papers / ongoing works:

a) Superconcentration and Related Topics (S. Chatterjee)

b) Chaos, concentration and multiple valleys in first-passage percolation (D. Ahlberg, M. Deijfen and M. Sfragara)

c) Superconcentration for minimal surfaces in first passage percolation and disordered Ising ferromagnets (B. Dembin and C. Garban)

d) Spin glass phase at zero temperature in the Edwards-Anderson model (S. Chatterjee)

e) Extremal decomposition of the free state of the Ising model on a regular tree -- sensibility of the overlap to boundary conditions (L. Coquille, C. Kuelske and A. Le Ny)

**(3)** How to go to Institut Fourier: From Grenoble main station, take Tram B (towards Gières) and get off at "Bibliothèques Universitaires" (this will take between 20 and 25 minutes). Then walk during 1 minute: the lab is just behind the restaurant "Le Martin's".

**(4)** In case you need ideas for hotels: We can tell you that the Fourier Institute is used to booking rooms in various hotels including the following: Residhotel Grenette (12 Rue de Palanka, 38000 Grenoble), Residhotel Le Central'Gare (8 Pl. de la Gare, 38000 Grenoble), The Originals Résidence - Grenoble Université (46 Av. Gabriel Péri, 38400 Saint-Martin-d'Hères), Hôtel des Alpes (45, Av. Félix Viallet, 38000 Grenoble).

*If you have any question, please send an email to hugo.vanneuville [at] univ-grenoble-alpes [dot] fr*

*[Attention : cette conférence ne parlera pas de cela.]*

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