Two new papers on essential dimension

Updated June 10, 2016 I have two new papers out, both joint with Bob Guralnick: Spinors and essential dimension: We show that certain representations of the spin group Spinn are generically free for n > 14 and calculate the generic stabilizer for n ≤ 14, for all base fields. This shows that the formula for the…

D_n diagram

New preprint on p-indexes of algebraic groups

New preprint out now: Tits p-indexes of algebraic groups, joint with Charles De Clercq. We give a `localized at a prime p‘ version of the results in Jacques Tits‘s classic 1966 paper Classification of semisimple algebraic groups. In that paper, he introduced the index of a semisimple group and classified all the possible values it…

Copyright: MFO

Volume in honor of Alexander Merkurjev

Happy 60th birthday to Alexander Merkurjev! A special volume of Documenta Mathematica in honor of the occasion has just been published. I have known Sasha for my whole career and he was my mentor during my UCLA postdoc. I am delighted to have been an editor for this volume in his honor. If you order…


“Luck” paper published

My paper Some people have all the luck, giving the details about the mathematical analysis behind Lawrence Mower’s 2014 expose of the Florida Lottery, has appeared. (See also this description from MAA FOCUS.) Our analysis has since been applied to identify criminals in many other states. This paper was written with Richard Arratia (USC), Lawrence…


“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…


New preprint on outer automorphisms of simple groups

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…

Skip Garibaldi on CBS Philly evening news

More frequent lottery winners in PA & NJ

CBS Philly investigated “too frequent” lottery winners in Pennsylvania and New Jersey. You can watch the story by Charlotte Huffman on the station’s webpage.  I helped them with the analysis.  For Pennsylvania the details are similar to the one I did for Florida, which relies on the BKR inequality and log-concavity of the regularized Beta…


New preprint on orthogonal representations of reductive groups

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…


“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…

Indy lottery story

Even Hoosiers are up to something with the lottery

The Indiana Lottery has said it will improve its security procedures in response to an ABC News 6 (WRTV Indianapolis) story.  The station, with my assistance, investigated frequent lottery winners in Indiana and found several who had claimed “suspiciously many” prizes and were affiliated with lottery retailers.