E8 survey to appear in Bulletin of the AMS

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…

“Simple groups stabilizing polynomials” paper published

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…

“Shells” paper to appear in Duke

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…