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In theoretical computer science, an increasingly important role is being played by sparse high-dimensional expanders (HDXs), of which we know two main constructions: "building" HDXs [Ballantine'00, ...] and "coset complex" HDXs [Kaufman--Oppenheim...

Let A be an abelian variety over a number field E ⊂ ℂ. We prove that, after replacing E by a finite extension, the action of Gal(Ē/E) on the ℓ‑adic Tate modules of A gives rise to a strongly compatible system of ℓ‑adic representations valued in the...

TBD

The theory of hierarchically hyperbolic groups, due to Behrstock, Hagen, and Sisto, was developed by abstracting work of Masur and Minsky on mapping class groups. Study of the large scale geometry of the outer automorphism group $\operatorname{Out}...