This seminar will focus on Diophantine problems in a broad sense, with a view towards (but not limited to) interactions between Number Theory and Logic. Particular attention will be given to topics with the potential of further developments in the context of this MSRI scientific program. This will provide an opportunity for researchers to update on new results, techniques and some of the main problems of the field.
To participate in this seminar, please register here: https://www.msri.org/seminars/25206
The classical Borel--Dwork rationality criterion provides a sufficient condition for a formal power series of rational coefficients to be (the Taylor expansion of) a rational function in terms of its radii of convergence (in some quotient representation) at all places. There are various generalizations of this criterion; in particular, a special case of the Grothendieck--Katz p-curvature conjecture is proved by Chudnovsky--Chudnovsky, André, and Bost using their algebraicity criteria, which are generalizations of the Borel--Dwork criterion. In this talk, I will recall the p-curvature conjecture and these algebraicity criteria and then I will discuss some other applications of these criteria. Part of the talk is based on the joint work in progress with Frank Calegari and Vesselin Dimitrov on p-adic zeta values.
To participate in this seminar, please register here: https://www.msri.org/seminars/25206No Notes/Supplements Uploaded No Video Files Uploaded