41 citations · 453 across the 49 of their papers we have counts for
49 papers
Root of the generic cubic as a power series in the discriminant
Jason Bland, Skip Garibaldi, Joel Rosenberg
An observation of J-P. Serre implies that the generic monic cubic polynomial, unique among generic monic polynomials of degree at least two, has a root that is a power series in th…
The longest and shortest roots of a real cubic
Jason Bland, Skip Garibaldi, Joel Rosenberg
There are many formulas in the literature providing roots of a real cubic that avoid some of the well-known pathologies of Cardano's formulas. Among these, we identify two that con…
Finding good bets in the lottery, and why you shouldn't take them
Aaron Abrams, Skip Garibaldi
We give a criterion under which the expected return on a ticket for certain large lotteries is positive. In this circumstance, we use elementary portfolio analysis to show that an…
Solutions to the exercises from the book "Albert algebras over commutative rings"
Skip Garibaldi, Holger P. Petersson, Michel L. Racine
This document presents the solutions to the exercises in the book "Albert algebras over commutative rings" published by Cambridge University Press, 2024, as well as errata and adde…
Invariant derivations and trace bounds
Skip Garibaldi, Robert M. Guralnick, Eric M. Rains
About 20 years ago, J-P.~Serre announced a bound on the trace of elements of compact Lie groups under the adjoint representation together with related results, provided indications…
Pictures of compact Lie groups (after Serre)
Skip Garibaldi
We fill in the details in a procedure outlined by Serre for drawing pictures of compact real Lie groups. In the case of Sp(), the picture generated by the method is connected w…