Title: Profinite descent for Picard spaces and groups in K(n)-local chromatic homotopy theory Abstract: The study of Picard groups in homotopy theory was initiated by Hopkins-Mahowald-Sadofsky. They gave a general framework […]
Title: The asymptotic behavior of eigenfunctions on symmetric spacesAbstract: Let X be a compact locally symmetric space, and Y a locally symmetric subspace. Let f be an eigenfunction of the […]
Title: On stable transfer operators and functorial transfer kernels Abstract: Langlands introduced stable transfer operators as a fundamental part of his proposal of Beyond Endoscopy. They are intended to be […]
Title: Number-theoretic methods to produce counterexamples for questions motivated by PDE’s.Abstract: In 1980 Carleson posed a question in PDE’s: how “well-behaved” must an initial data function be, to guarantee pointwise convergence […]
Title: Number-theoretic methods to produce counterexamples for questions motivated by PDE’s.Abstract: In 1980 Carleson posed a question in PDE’s: how “well-behaved” must an initial data function be, to guarantee pointwise convergence […]
Title: Automorphic Galois representations for classical groupsAbstract: It is a theorem due to many people, most recently by Harris-Lan-Taylor-Thorne and Scholze, that there exist Galois representations associated with regular cuspidal automorphic […]
Title: Automorphic Galois representations for classical groupsAbstract: It is a theorem due to many people, most recently by Harris-Lan-Taylor-Thorne and Scholze, that there exist Galois representations associated with regular cuspidal automorphic […]
Title: Categorical diagonalization.Abstract: We give an introduction to the circle of ideas known as categorification, guided by the following question: what might it mean to diagonalize a functor?Given a category, one […]
Title: Categorical diagonalization.Abstract: We give an introduction to the circle of ideas known as categorification, guided by the following question: what might it mean to diagonalize a functor?Given a category, one […]
Title: Decomposition problem for topological Azumaya algebras with an involution of the first kindAbstract: Topological Azumaya algebras (TAAs) over a space are topological shadows of more complicated algebraic Azumaya algebras […]
Title: A fourth-order Escobar-Yamabe problem on a half-ballAbstract: The celebrated Yamabe problem asks us to make a conformal change on a compact Riemannian manifold such that the scalar curvature becomes […]
Title: Local-global compatibility over function fields Abstract: We show that V. Lafforgue's global Langlands correspondence is compatible with Fargues–Scholze's semisimplified local Langlands correspondence. As a result, we canonically lift Fargues–Scholze's construction […]