The n-Category Café

• Projective geometry and the exceptional Jordan algebra.

Abstract. Dubois-Violette and Todorov noticed that the gauge group of theStandard Model of particle physics is the intersection of two maximal subgroups of $\text{F}_4$. which is the automorphism group of the exceptional Jordan algebra $\mathfrak{h}_3(\mathbb{O})$. Here we conjecture that these can be taken to be any subgroups preserving copies of $\mathfrak{h}_2(\mathbb{O})$ and $\mathfrak{h}_3(\mathbb{C})$ that intersect in a copy of $\mathfrak{h}_2(\mathbb{C})$. Given this, we show that the Standard Model gauge group consists of all isometries of the octonionic projective plane that preserve an octonionic projective line and a complex projective plane intersecting in a complex projective line. This is joint work with Paul Schwahn.

This is an introductory talk for mathematicians. Physicists may prefer the two talks here. Those go much further in some ways, but they don’t cover the new ideas that Paul Schwahn and I are in the midst of working on.