New preprint out today: Outer automorphisms of algebraic groups and a Skolem-Noether theorem for Albert algebras, written with Holger P. Petersson. In it, we study the question of existence of outer automorphisms of simple algebraic groups. One knows that the *-action and the Tits class provide obstructions to the existence of outer automorphisms, and the question is…
In my new preprint Bilinear and quadratic forms on rational modules of split reductive groups, written with Daniel K. Nakano, we extend the beautiful and classical theory of orthogonal and symplectic representations of split reductive groups in characteristic zero to prime characteristic. The two main new technical challenges are that orthogonal representations in characteristic 2 are connected with quadratic…
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…
My paper Asymptotic distribution for the birthday problem with multiple coincidences, via an embedding of the collision process, joint with Richard Arratia (a probabilist) and Joe Kilian (a computer scientist), will appear in the journal Random Structures & Algorithms. It contains several new results on the birthday problem: how many people do you need to have c birthdays in…
My paper Lottery-spending: a non-parametric analysis has appeared. This was written jointly with undergrads Kayla Frisoli, Li Ke, and Melody Lim, and describes the results of a project we did last spring. The problem is to understand those people who spend a lot on lottery tickets and how much they actually spend. We made use…
Skip Garibaldi and Kirill Zainoulline, “The γ-filtration and the Rost invariant”, Journal für die reine und angewandte Mathematik #696 (2014), 225-244. DOI: 10.1515/crelle-2012-0114
Hernando Bermudez, Skip Garibaldi, and Victor Larsen, “Linear preservers and representations with a 1-dimensional ring of invariants”, Transactions of the American Mathematical Society 366 #6 (2014), 4755-4780. DOI: 10.1090/S0002-9947-2014-06081-9
New preprint [arxiv.org:1310.7055], joint with Richard Arratia (a probabilist) and Joe Kilian (a computer scientist) on the birthday problem: how many people do you need to have c birthdays in common? Perhaps surprisingly, the results are new.
New paper at joint with Bob Guralnick: Simple algebraic groups are (usually) determined by an invariant (arxiv.org:1309.6611). A very special case of our main results is a description of groups of type E8. Update (6/3/2014): The paper now has a new title “Simple groups stabilizing polynomials”. Update (5/2015): It will be published in Forum of Mathematics, Pi.
New paper from my group: Degree 3 cohomological invariants of groups that are neither simply connected nor adjoint. [arxiv.org:1305.2899]