Seminar Event Detail


Colloquium Series

Date:  Tuesday, October 26, 2021
Location:  1360 East Hall (4:00 PM to 5:00 PM)

Title:  Rainich Lecture #1: 3987^{12} + 4365^{12} = 4472^{12} (almost)

Abstract:   Not quite! How do we produce such fake solutions? I will review work of several authors (Coppersmith, Elkies, Bombieri-Pila, Heath-Brown) about this, and the related question of bounding the number of integral solutions to a polynomial equation P(x1, ..., xn) = 0. I will then explain a recent result with Lawrence and Ellenberg (https://arxiv.org/abs/2109.01043) showing that integral points are "rare" on many natural moduli spaces.

Files:


Speaker:  Akshay Venkatesh
Institution:  Institute for Advanced Study

Event Organizer:     

 

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