Peter Connick

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 so much for this wonderful opportunity. SURF allowed me to work closely with three good friends on an incredibly interesting project, and none of this would have been possible without you. It is because of programs like these that students are able to be exposed to research at an undergraduate level and learn more about what is to be a researcher and a person as well. For me in particular, this project opened my eyes to new and exciting branches of research, and for that I am truly grateful.
  • Major: Physics and Math (math undeclared)
  • Sponsor: Sherrill Fund
  • Mentor: Richard Borcherds