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For general reductive groups over a p-adic number field, Fargues and Scholze constructed a (semi-simplified) local Langlands with many good properties. On the other hand, classical local Langlands correspondences are known for classical groups via endoscopy theory and theta lifting. We review…
Abstract: The presence of hyperbolic periodic orbits or invariant sets often has an effect on the global behavior of a symplectic dynamical system. In this talk we discuss two theorems along the lines of this phenomenon, extending some properties of Hamiltonian diffeomorphisms to dynamically…
Abstract: In positive characteristic, on one hand the quantum D-module (from Gromov--Witten theory) carries extra central endomorphisms known as quantum Steenrod operations. On the other hand, in representation theory, the algebra of differential operators also carry a "large center" in positive…
The cochlea is the main organ of the inner ear. It is responsible for converting the incoming mechanical sound signals from the middle ear into neural signals in the auditory nerve. This transformation involves a fascinating sequence of mechanical and hydrodynamical components, responsible for…