Kazhdan seminar: Ehud de Shalit - Difference Equations

Sun, 19/12/202111:00-12:45
Repeats every week every Sunday until Sat Jan 15 2022
Ross 70 & Zoom
Zoom link: 


Meeting ID: 891 7195 9478
Passcode: 161803

Description: I will go over recent work of Schafke and Singer on the rationality of power series satisfying a pair of q-difference equations with respect to multiplicatively independent
q's and their Mahler equations analogues. This work complements previous results by
Bezivin, Boutaba, Adamczewski and Bell, and is motivated by questions in transcendence 
theory. I will then go over work of mine from 2020, exploring the same questions over fields 
of elliptic functions. New phenomena arise and new methods are required. In the last
part of the seminar I will go over the preprint "Algebraic independence and linear difference
equations" by Adamczewski, Dreyfus, Hardouin and Wibmer, https://arxiv.org/abs/2010.09266, that uses methods from the Galois theory of difference equations to strengthen the earlier results over rational function fields. My hope is to gain insight into how this latter work might be carried over to the elliptic realm.

All the background on difference equations and their Galois theory will be fully explained.

Mailing list:  Dear all, I would like to make a mailing list of the participants, so that I do not bother everybody with mass mail.

If you want to be included, please send me a note saying "Include me in the mailing list".

The link to the recording of today's lecture on Zoom is