A framework for generating inequality conjectures

Abstract: In this talk, I'll present some recent and ongoing work, where we propose a systematic approach to finding abstract patterns in mathematical data, in order to generate conjectures about mathematical inequalities. We focus on strict inequalities of type $f < g$ and associate them with a Banach manifold. We develop a structural understanding of this conjecture space by studying linear automorphisms of this manifold. Next, we propose an algorithmic pipeline to generate novel conjecture. As proof of concept, we give a toy algorithm to generate conjectures about the prime counting function and diameters of Cayley graphs of non-abelian simple groups. Some of these conjectures were proved while others remain unproven.

machine learningmathematical physicscommutative algebraalgebraic geometryalgebraic topologycombinatoricsdifferential geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Machine Learning Seminar

Series comments: Online machine learning in pure mathematics seminar, typically held on Wednesday. This seminar takes place online via Zoom.

For recordings of past talks and copies of the speaker's slides, please visit the seminar homepage at: kasprzyk.work/seminars/ml.html