Writing math papers

Writing math papers is more like technical writing than writing essays, but general advice on technical writing only gets you so far.  For more advanced advice, Igor Pak offers his opinionated thoughts.  I especially recommend his tips on how to create a productive Final Remarks section. (Real beginners at writing math papers make a standard…

Essential dimension article named Editor’s Choice

My recent article Essential dimension of algebraic groups, including bad characteristic with Bob Guralnick was named an “Editor’s Choice“. As a consequence, it will be available free open access on the journal website for the next year. Here’s the abstract: We give upper bounds on the essential dimension of (quasi-) simple algebraic groups over an…

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…

"Optimization in Microeconomics" by Christopher Curran and Skip Garibaldi

New edition of “Optimization in microeconomics”

The publisher is making a new edition of Optimization in microeconomics! This is a textbook for a senior-level capstone course in mathematical economics. It was developed for Math/Econ 425 at Emory University.  The text is a polishing of the extensive course notes that economist Chris Curran developed over the many years that he taught that…

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…

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…

“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…