Modularity and Height Bounds

Introductory Workshop: Diophantine Geometry February 06, 2023 - February 10, 2023

February 09, 2023 (11:00 AM PST - 12:00 PM PST)

Speaker(s): Hector Pasten (Pontificia Universidad Católica de Chile)
Location: SLMath: Eisenbud Auditorium, Online/Virtual

Tags/Keywords

modularity
elliptic curves
height bounds

Primary Mathematics Subject Classification

Secondary Mathematics Subject Classification

11M36 - Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas)
11E76 - Forms of degree higher than two

Video

Modularity And Height Bounds

Abstract

In this talk I will explain how the modularity of elliptic curves leads to height bounds of different sorts. These have applications in explicit computation of integral points in varieties, and proving unconditional results related to the abc conjecture.

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Modularity And Height Bounds

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