SURF

Aidan Backus

Investigating Root-Multiplicities of Kac-Moody Algebras

Over the summer, we propose to investigate the root multiplicities of (generalized) Kac-Moody Algebras. Our plan is to create an open-source computer package that allows for the computation of root multiplicities of Kac-Moody algebras, building upon the existing tools available to computational mathematicians, for instance, the popular library sage-math. Once we have developed and verified this package against known tables of root multiplicities, we aim to start investigating the root multiplicities of simple graphs, and attempt to address some outstanding conjectures on the distributions of root multiplicities. A greater understanding of the root multiplicities of Kac-Moody algebras would help with questions such as finding natural geometrical realizations of the algebras, and shed light on the connections that have already been found with mathematical physics. Some of these applications may include generalised knot invariants defined over Kac-Moody algebras rather than Lie Algebras, or the study of symmetries of systems and spaces that are not finite-dimensional.

Message to Sponsor

Thank you for your support! My work with SURF has introduced me to areas of mathematics that I would have never considered otherwise -- it felt a bit like stepping into a dark cave unexplored by the likes of men, and fumbling around in anticipation of finding a light. This is very different than my past research, which was very closely guided, in that I had a lot more freedom to study what I thought was interesting, but in exchange, had fewer options if I got stuck. And so this was a valuable learning experience, and a much better simulation of graduate school than previous work of mine. I hope to continue some of this work throughout the school year.
  • Major: Mathematics
  • Sponsor: Sherrill Fund
  • Mentor: Richard Borcherds