Le Séminaire Différentiel a vu le jour en 2003 à l’IMJ sous l’impulsion de Daniel Bertrand. Depuis 2018, il est co-organisé par Alin Bostan et Lucia Di Vizio. Les séances ont lieu en alternance entre Paris et Versailles, à raison d'un mardi par semestre et de 3 exposés par réunion, avec le soutien du Laboratoire de Mathématiques de Versailles, de l'INRIA, du GDR EFI et du projet ANR EAGLES.

Prochaine journée le 14 avril 2026 à l'IHP (salle Yvette Cauchois, bâtiment Perrin)  

Pour vous inscrire au repas, merci de remplir ce formulaire: https://framaforms.org/inscription-a-la-journee-du-seminaire-differentiel-du-14-avril-2026-a-lihp-1773829209

10h30-11h30 Sergey Yurkevich (A&R Tech, Vienna, Austria),  When is a hypergeometric function algebraic?
Abstract: The classification of algebraic hypergeometric functions is a classical problem with seminal results going back to Schwarz and Landau. In this talk I will give an overview on the history of the question and in particular present Schwarz' list and the famous interlacing criterion of Christol (1986) and Beukers–Heckman (1989). I will also showcase a complete decision procedure for the algebraicity of hypergeometric functions with no restriction on their set of parameters. This talk is based on joint work with Florian Fürnsinn.
14h15-15h15 Kilian Raschel (LAREMA, Université d'Angers), Singular walks in the quarter plane, Bernoulli numbers and differential transcendences 
Abstract: In combinatorics, and more specifically in the study of lattice walks confined to cones such as the quarter plane, it has become standard to investigate the differential nature of the associated generating functions. When these functions are differentially finite or differentially algebraic, one can derive concrete information about the model, including asymptotics, recurrences, and, in some cases, closed-form expressions. By contrast, the combinatorial significance of differential transcendence remains much less understood.
In this talk, I will present a family of examples for which we provide a combinatorial and probabilistic interpretation of differential transcendence. Focusing on singular walks in the quarter plane, we show that, while the generating function is generically differentially transcendental, it exhibits a stronger form of differential transcendence at the spectral radius. This phenomenon is explained by an underlying probabilistic critical behavior.
This is joint work with Alin Bostan and Lucia Di Vizio (arXiv:2504.13542).
15h30-16h30 Veronica Fantini (LMO, Université Paris-Saclay), Resurgence and Borel summability for thimble integrals
Abstract: In this talk, I will review the resurgence and summability properties of divergent series coming from the asymptotic expansion of the so-called thimble integrals, namely, integrals of the form $\int_{\mathcal{C}} e^{-f/\hbar} \, \nu\,$, where $\mathcal{C}$ is the steepest-descent contour (Lefschetz thimble) from a critical point of the function $f$. The first class of examples is when $f$ is a rational function: in this case, these integrals provide analytic solutions to differential equations with irregular singularities (for example, the Airy function) and coincide with suitable resummations of the corresponding formal solutions. More generally, the function $f$ can be multi-valued, and if time permits, I will discuss some examples. 

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