In Spring 2026, we will continue the long tradition of the Kolchin Seminar in Differential Algebra at the City University of New York (see here for the past talks) with an online seminar. To obtain the Zoom link, please register via the following link:
Register to attend the online Kolchin seminar
You will then receive a weekly e-mail reminder a few days before the seminar, including title and abstract of the talk. If you already registered for the seminar last semester, you do not need to register again. In case you are interested in giving a talk in this seminar, please contact the organizers.
The seminar meets weekly, every Friday 10:00 am New York time. We will have a 40 minute talk, followed by questions.
Algebraic theory of differential and difference equations (Galois theory, differential and difference algebra, integrability), algorithms and their implementation, connections to model theory, and applications (such as mathematical biology, numerical analysis of ODEs and PDEs, motion planning, etc.)
Spring 2026 Organizers:
Title: The Carlitz module and a differential Ax-Lindemann-Weierstrass theorem for the Euler gamma function
We prove an Ax-Lindemann-Weierstrass differential transcendence result for Euler's gamma function, namely that the functions Γ(ν-ζ1(ν)),…, Γ(ν-ζn(ν)) are differentially independent over the field of rational functions in the variable ν, with coefficients in the field k of 1-periodic meromorphic functions over the complex numbers, as soon as ζ1,…, ζn determine a set of algebraic functions over k, stable by conjugation and pairwise distinct modulo the integers.
To prove this result we use both the Galois theory of difference equations and the theory of a characteristic zero analog of the Carlitz module introduced by the second author in 2013. As an intermediate result we give an explicit description of the Picard-Vessiot rings and of the Galois groups associated to the operators in the image of the Carlitz module, using techniques inspired by the Carlitz-Hayes theory. This is a joint work with Federico Pellarin.
See the talks from past years.