**Dates**: November 27 – December 1 (“Special week”), December 4–8 (“Workshop”), December 11 (“Topical Day”)

**How to come to IHP** /
**Some restaurants close to IHP**

#### Special week

*November 27 to December 1, 2023*

**Creative Telescoping**(long course, Monday to Friday, 9:30-12:00, Amphitheater Darboux), S. Chen, M. Kauers, and C. Koutschan**Advanced Determinant Calculus**(short course, Monday and Tuesday, afternoon), C. Krattenthaler**General audience presentation***On Fermat’s penultimate theorem*, Wednesday 16:00-17:00, X. Caruso**Special session of the Differential Seminar**, Thursday and Friday, 15:00-17:00

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

*December 4 to 8, 2023*

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

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.

**Invited speakers**

- Arvind Ayyer (Bangalore, India):
*The multispecies totally asymmetric long-range exclusion process and Macdonald polynomials* - Mireille Bousquet-Mélou (Bordeaux, France):
*Some applications of computer algebra in enumerative combinatorics* - Jehanne Dousse (Geneva, Switzerland):
*Partition identities, functional equations and computer algebra* - Tony Guttmann (Melbourne, Australia):
*Self-avoiding walks in a square and the gerrymander sequence* - Charlotte Hardouin (Toulouse, France):
*Galois group for large steps walks* - Mark van Hoeij (Tallahassee, Florida, USA):
*Linear Difference Equations, generalizing Liouvillian Solutions* - Stephen Melczer (Waterloo, Canada):
*New Software for Analytic Combinatorics* - Igor Pak (Los Angeles, USA):
*TBA* - Veronika Pillwein (Hagenberg, Austria):
*Proving positivity for P-recursive sequences* - Gleb Pogudin (Palaiseau, France):
*Quadratizations of differential equations* - Dan Romik (California, USA):
*TBA* - Carsten Schneider (Hagenberg, Austria):
*Summation Tools for Combinatorics and Elementary Particle Physics* - Alan Sokal (London, UK):
*Some problems I’d like solved, from a user of computer algebra* - Pierre Vanhove (Saclay, France):
*Efficient algorithms for differential equations satisfied by Feynman integrals* - Michael Wallner (Vienna, Austria):
*Stretched exponentials and beyond* - Nicholas Witte (Wellington, New Zealand):
*Beyond Painlevé: The need for computational tools to reveal hidden structure*

#### Topical day: Elimination for Functional Equations

*December 11, 2023*

**Organizer:** G. Pogudin

**Speakers:** Hadrien Notarantonio,
André Platzer,
Daniel Robertz,
Sonia Rueda,
Alexandros Singh,
Nathalie Verdière