#### Special week

*November 27 to December 1, 2023*

**Creative Telescoping**(long course, Monday to Friday), S. Chen, M. Kauers, and C. Koutschan**Computer Algebra for Walks**(short course, Monday and Tuesday), A. Bostan**General audience presentation**, Wednesday 29th, X. Caruso

#### Computer Algebra for Functional Equations in Combinatorics and Physics

**Organizers**: A. Bostan,
J. Bouttier,
T. Cluzeau, L. Di Vizio, C. Krattenthaler, J.-M. Maillard.

*December 4 to 8, 2023*

In many areas of pure and applied mathematics, as well as in computer science and in theoretical physics, functional equations form either the object of study or important tools for applications. We are currently experiencing increasingly strong interactions between theory and applications, many common actions having taken place over the past ten years. By functional equations, we mean mainly ordinary differential equations, with differences, with $q$-differences, Mahlerian, linear or algebraic, possibly multivariate. For instance, nonlinear algebraic differential equations emerge naturally in integrable models in physics (Painlevé equations, Schlesinger systems, KdV equations, etc., associated with Lax pairs, Yang-Baxter equations,…). All these types of functional equations have been and are still very actively studied from many points of view, using algebraic, arithmetic and geometric tools. A recent trend is that computer algebra algorithms are more and more used to solve functional equations arising in enumerative combinatorics and in statistical physics. Notable examples come from questions related to lattice walks. In combinatorics, basic objects like trees, maps, permutations, and Young tableaux can be represented by models of walks confined to cones. In physics, many objects, including polymers and queueing models, are accurately modeled by walks on lattices, particularly those evolving in cones with several boundaries. This workshop brings together representatives from the three different communities (computer algebra, combinatorics and theoretical physics) to discuss longstanding conjectures, to learn each other’s techniques and to plan the directions for the future.

#### Topical day: Computer Algebra in Statistical Physics

*December 11, 2023*

**Organizer:** A. Sportiello