Amir Livne Bar-on | Searcharxiv

arXiv2025

The Equational Theories Project: Advancing Collaborative Mathematical Research at Scale

We report on the Equational Theories Project (ETP), an online collaborative pilot project to explore new ways to collaborate in mathematics with machine assistance. The project successfully determined all 22 028 942 edges of the implication graph between the 4694 simplest equational laws on magmas, by a combination of human-generated and automated proofs, all validated by the formal proof assistant language Lean. As a result of this project, several new constructions of magmas satisfying specific laws were discovered, and several auxiliary questions were also addressed, such as the effect of restricting attention to finite magmas.

math.RA↗

arXiv2013

The (B) conjecture for uniform measures in the plane

We prove that for any two centrally-symmetric convex shapes $K,L \subset \mathbb{R}^2$, the function $t \mapsto |e^t K \cap L|$ is log-concave. This extends a result of Cordero-Erausquin, Fradelizi and Maurey in the two dimensional case. Possible relaxations of the condition of symmetry are discussed.

math.FA↗