6 papers
Categorical Bass-Serre Theory for Tree Quotients
Jiacheng Tang
We develop a categorical framework for Bass-Serre theory, which recovers parts of classical and profinite Bass-Serre theories for tree quotients. More precisely, we show that in wh…
Profinite Cosheaves Valued in Pro-regular Categories
Jiacheng Tang
We prove that the category of profinite cosheaves valued in a pro-regular category (satisfying mild assumptions) is itself canonically a pro-completion. As a corollary, we extend W…
Coproducts Internal to Profinite Spaces
Jiacheng Tang
We give a categorical explanation for many properties of profinite coproducts of profinite groups, which were previously proven on a case-by-case basis. All of these properties tak…
Quantum-Noise Induced Localization and Motional Squeezing in a Rydberg Quantum Simulator
Benno Bock, Daniel Brady, Michael Fleischhauer
We investigate the interplay between mechanical forces and the internal-state dynamics of Rydberg excitations in atom-tweezer arrays. Dipole interactions between Rydberg atoms faci…
Open Condensed Subgroups and Mackey's Formula
Jiacheng Tang
We define what it means for a condensed group action to be open (following Scholze) and show that for open subgroups, many elementary results about abstract modules hold for conden…
Profinite and Solid Cohomology
Jiacheng Tang
Solid abelian groups, as introduced by Dustin Clausen and Peter Scholze, form a subcategory of all condensed abelian groups satisfying some ''completeness'' conditions and having f…