Speaker: Dylan Thurston (Harvard)
Title: The Exceptional Series and Magic Triangle of Lie Algebras
Abstract: Cvitanovic in 1977 and Deligne in 1996 independently discovered commonalities among all the exceptional Lie algebras, forming a kind of "series" analogous to the classical sl(n) and o(n) series; Deligne conjectured that this series can be extended to a family depending on a continuous (!) parameter, specializing to the exceptional Lie algebras at the known points. Cvitanovic furthermore fit these series into a Magic Triangle, extending Freudenthal's Magic Square. Following Deligne and Gross, we clarify where this Magic Triangle comes from and investigate whether several rows have more points on them; this further extends the Magic Triangle to include some super Lie algebras.