Title	Diagonals, congruences, and algebraic independence
Creator	Adamczewski, Boris
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2017-09-19T14:01
Description	A very rich interplay between arithmetic, geometry, transcendence and combinatorics arises in the study of homogeneous linear differential equations and especially of those that “come from geometry” and the related study of Siegel G-functions. A remarkable result is that, by adding variables, we can see many transcendental G-functions (and thus many generating series) as arising in a natural way from much more elementary function, namely rational functions. This process, called diagonalization, can be thought of as a formal integration. I will discuss some properties enjoy by diagonals of rational functions and connect them with Lucas'congruences for binomial coefficients and algebraic independence of power series. This corresponds to some joint works with Jason Bell and Eric Delaygue.
Extent	63 minutes
Subject	Mathematics; Combinatorics; Sequences, series, summability; Discrete mathematics
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: Institu Camille Jordan & CNRS
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2018-03-31
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0364598
URI	http://hdl.handle.net/2429/65042
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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Diagonals, congruences, and algebraic independence Adamczewski, Boris

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