SageMath experiments in Differential and Complex Geometry

TL;DR

This paper demonstrates how SageMath can assist in research on complex and differential geometry by exploring classification problems related to Lie group quotients, cohomological invariants, and geometric structures.

Contribution

It showcases practical applications of SageMath in complex geometry research, focusing on classification problems and computational approaches.

Findings

SageMath effectively computes cohomological invariants.

It aids in classifying geometric structures on Lie group quotients.

The paper provides example applications, not original research results.

Abstract

This note summarizes the talk by the author at the workshop "Geometry and Computer Science" held in Pescara in February 2017. We present how SageMath can help in research in Complex and Differential Geometry, with two simple applications, which are not intended to be original. We consider two "classification problems" on quotients of Lie groups, namely, "computing cohomological invariants" [D. Angella, M. G. Franzini, F. A. Rossi, Degree of non-K\"ahlerianity for 6-dimensional nilmanifolds, Manuscripta Math. 148 (2015), no. 1-2, 177--211], [A. Latorre, L. Ugarte, R. Villacampa, On the Bott-Chern cohomology and balanced Hermitian nilmanifolds, Internat. J. Math. 25 (2014), no. 6, 1450057, 24 pp.], and "classifying special geometric structures" [D. Angella, G. Bazzoni, M. Parton, Structure of locally conformally symplectic Lie algebras and solvmanifolds, arXiv:1704.01197.], and we set the problems to be solved with SageMath.