11 Giugno 2026 | Lezione Lagrangiana: Umberto Zannier (Scuola Normale Superiore di Pisa)
Pubblicato: Martedì 14 aprile 2026
Lezione lagrangiana
On a problem of Polya and some of its evolutions.
Umberto Zannier
Scuola Normale Superiore di Pisa
Data e luogo:
11 Giugno 2026 dalle 14.30 alle 15.30
presso Palazzo Campana, Aula Magna
Abstract
Around 1921 Polya asked about the algebraicity of the indefinite integral of an algebraic function, in terms of the integrality of the coefficients in a power-series expansion. Polya nicely answered the special case of rational functions, using Fermat's congruence.
Though the formulation was very simple, the general case was solved only much later by transcendence techniques.
The question is also linked with a simply stated well-known local-global conjecture of Grothendieck on linear differential equations over polynomial rings, and with other number-theoretical issues.
We shall survey on the topic, also illustrating (if time allows) novel questions arising from a different approach to Polya's issue, and some answers given recently by Katz, and the speaker.
Short Bio
Umberto Zannier is Professor at the Scuola Normale Superiore in Pisa and one of the leading experts in Number Theory and Diophantine geometry. He was a visiting professor at several institutions, including: Institute for Advanvced Study, Institut Henri Poincaré, ETH Zurich, and Erwin Schrödinger Institute. Invited speaker at the International Congress of Mathematicians in 2014 in Seoul and recipient of an ERC Advanced Grant, he is a member of the Accademia Nazionale dei Lincei and Academia Europaea.