Experimentation at the Frontiers of Reality in Schubert Calculus

TL;DR

This paper presents a scalable computational framework for large-scale experiments in mathematics, demonstrated through extensive experiments in real Schubert calculus to aid in conjecture formulation and testing.

Contribution

It introduces a general framework for large-scale mathematical experiments using common university computer resources, enabling extensive computational exploration in Schubert calculus.

Findings

Solved over 1.1 billion polynomial systems

Consumed over 350 GHz-years of computing

Enabled new conjecture testing in real Schubert calculus

Abstract

We describe a general framework for large-scale computational experiments in mathematics using computer resources that are available in most mathematics departments. This framework was developed for an experiment that is helping to formulate and test conjectures in the real Schubert calculus. Largely using machines in instructional computer labs during off-hours and University breaks, it consumed in excess of 350 GigaHertz-years of computing in its first six months of operation, solving over 1.1 billion polynomial systems.