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.

Balls in bins

“Birthday problem” paper to appear in Random Structures & Algorithms

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…


Lottery spending analysis paper published

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…

San Diego Air & Space Museum logo

MathAlive! comes to San Diego

MathAlive! will open at the San Diego Air & Space Museum on January 31st and run through September.  This exhibit aims to show kids unexpected ways that math appears in recreation as well as in working life, promising “unique, interactive experiences to transform math from its native form into the fascinating applied worlds of design,…

Air Force logo

Joining the Air Force Scientific Advisory Board

I have been appointed to the Air Force Scientific Advisory Board, and I will be formally sworn in this January.  I’m excited by this opportunity to serve, and to do so with such accomplished experts from such varied backgrounds. The Board’s purpose is to provide independent advice and recommendations to the Secretary of Defense and the Secretary of the Air…

New Jersey lottery clerk

Suspicious lottery winners investigated in New Jersey

Shannon Mullen of the Asbury Park Press uncovered several lottery New Jersey lottery retailers who have won suspiciously many lottery prizes, see the story here.  I helped with the analysis. Update (12/12/14): As a consequence of the Asbury Park Press story, New Jersey Assemblyman Burzichelli says the state Legislature should take a closer look. Update (2/18/15): And now…