The end of the paper “Finite H-spaces and Lie groups” by J.F. Adams (Journal of Pure and Applied Algebra, vol. 19 (1980)) contains the following, amazing purported “Letter from E8”. Gentlemen, Mathematicians may be divided into two classes; those who know and love Lie groups, and those who do not. Among the latter, one may…
My survey E8, the most exceptional group will appear in an upcoming issue of Bulletin of the American Mathematical Society. It talks about the history and recent results on E8, focusing on the algebraic perspective of Lie algebras, Lie groups, and algebraic groups. You can read the article here or get an inkling of some the…
My paper “Simple groups stabilizing polynomials“, written with Bob Guralnick, has appeared in Forum of Mathematics Pi. In it, we show that, if a simple algebraic group G stabilizes a polynomial function f on a vector space V, then with a very short list of exceptions G is actually the identity component of the stabilizer of f. We give various concrete applications of…
My paper Shells of twisted flag varieties and the Rost invariant, joint with Victor Petrov and Nikita Semenov, will appear in Duke Mathematical Journal. We introduce new techniques for studying the Krull-Schmidt decomposition of mod p Chow motives of projective homogeneous varieties, by generalizing Vishik’s notion of shells on quadrics to arbitrary projective homogeneous varieties. We then apply our techniques…
Thanks to everyone who came out for my plenary address “E8 and other exceptional groups” at the AMS meeting in Greensboro, NC!