Classical Mechanics and Diophantine Equations

17 January 2022
16:00
Jay Swar
Abstract

We'll sketch how the $K$-rational solutions of a system $X$ of multivariate polynomials can be viewed as the solutions of a "classical mechanics" problem on an associated affine space.

When $X$ has a suitable topology, e.g. if its $\mathbb{C}$-solutions form a Riemann surface of genus $>1$, we'll observe some of the advantages of this new point of view such as a relatively computable algorithm for effective finiteness (with some stipulations). This is joint work with Minhyong Kim.
 

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

  • Junior Number Theory Seminar