Let $H_n$ be the one-dimensional Honda formal group of height $n$ over $mathbf F_{p^n}$ and let [ R_n=W(mathbf F_{p^n})[[u_1,ldots,u_{n-1}]],qquad A_n=R_n/(p). ] We prove, for every height $n$ and every prime $p$, that the prime ideals of $A_n$ stable und...

Autoformalisation is increasingly used to verify mathematical texts, including those generated by AI, as in OpenAI's announced proof of blow-up of solutions to the Navier-Stokes equations. In this process, an AI system translates the text from a natural l...

Together with Bourgain's slicing problem and the variance conjecture, the Kannan-Lovász-Simonovits (KLS) conjecture has been a driving force for mathematical developments in high dimensional geometry in recent decades. We present here a proof of this conj...