In this talk we survey an algebro-homotopical perspective on classical gauge field theories in the perturbative regime. We show how cyclic $L_\infty$-algebras encode their essential structures, among them fields, symmetries, and actions. We illustrate this perspective through three central examples: Maxwell's electromagnetism, Chern-Simons theory, and Yang-Mills theory.

Let $H$ be a subgroup of $(\mathbb{Z}_2)^m$ acting on a real moment-angle complex. In this talk, I will discuss when the H-action is equivariantly formal and how this follows from similar results on torus actions on moment-angle complexes. As an application, I will discuss the cohomology of subgroups of Right-Angled Coxeter Groups. This talk is based on ongoing joint work with S. Amelotte.

I will briefly discuss some of the essential concepts that one speaks of in the theory of sheaves on the small etale sites of schemes, such as the etale fundamental group, locally constant sheaves, ell-adic sheaves, etale cohomology, and ell-adic cohomology. Time permitting, I will also state theorems about ell-adic cohomology such as the Grothendieck-Lefschetz Trace Formula, Poincare duality, and the Weil conjectures.