相关论文: Fr\'echet completions of moderate growth old and (…

The first main result is that the Casselman-Wallach Globalization of a real analytic family of Harish-Chandra modules is continuous in the parameter. Our proof of this result uses results from the thesis of Vincent van der Noort in several…

The Casselman-Wallach theorem is a foundational result in the theory of representations of real reductive groups connecting algebraic representations to topological representations. We provide a quantitative version of this theorem. For…

Eisenstein series are ubiquitous in the theory of automorphic forms. The traditional proofs of the meromorphic continuation of Eisenstein series, due to Selberg and Langlands, start with cuspidal Eisenstein series as a special case, and…

We show that doubling at some large scale in a Cayley graph implies uniform doubling at all subsequent scales. The proof is based on the structure theorem for approximate subgroups proved by Green, Tao and the first author. We also give a…

A group presentation is said to have rational growth if the generating series associated to its growth function represents a rational function. A long-standing open question asks whether the Heisenberg group has rational growth for all…

An interpretation of the Casselman-Wallach (C-W) Theorem is that the $K$-finite functor is an isomorphism of categories from the category of finitely generated, admissible smooth Fr\'echet modules of moderate growth to the category of…

Freiman's theorem asserts, roughly speaking, if that a finite set in a torsion-free abelian group has small doubling, then it can be efficiently contained in (or controlled by) a generalised arithmetic progression. This was generalised by…

This paper presents a simplified geometric proof of the Molino-Alexandrino-Radeschi (MAR) Theorem, which states that the closure of a singular Riemannian foliation on a complete Riemannian manifold is itself a smooth singular Riemannian…

This paper is a follow-up to our joint paper with I. Agol, P. Storm and K. Whyte "Finiteness of arithmetic hyperbolic reflection groups". The main purpose is to investigate the effective side of the method developed there and its possible…

For any Lie supergroup whose underlying Lie group is reductive, we prove an extension of the Casselman-Wallach globalisation theorem: There is an equivalence between the category of Harish-Chandra modules and the category of…

A version of group cohomology for locally compact groups and Polish modules has previously been developed using a bar resolution restricted to measurable cochains. That theory was shown to enjoy analogs of most of the standard algebraic…

The purpose of this paper is two-fold: we systematically introduce the notion of Cheeger deformations on fiber bundles with compact structure groups, and recover in a very simple and unified fashion several results that either already…

Given a Noetherian formal scheme $\hat X$ over ${\rm Spf}(R)$, where $R$ is a complete DVR, we first prove a theorem of meromorphic descent along a possibly infinite cover of $\hat{X}$. Using this we construct a specialization functor from…

We sketch a proof of a conjecture of [FFKM] that relates the geometric Eisenstein series sheaf with semi-infinite cohomology of the small quantum group with coefficients in the tilting module for the big quantum group.

For any holomorphic function $f\colon X\to \mathbb{C}$ on a complex manifold $X$, we define and study moderate growth and rapid decay objects associated to an enhanced ind-sheaf on $X$. These will be sheaves on the real oriented blow-up…

Let $G$ be a real linear reductive group and $K$ be a maximal compact subgroup. Let $P$ be a minimal parabolic subgroup of $G$ with complexified Lie algebra $\mathfrak{p}$, and $\mathfrak{n}$ be its nilradical. In this paper we show that:…

The goal of this series of papers is to give a new non-commutative approach to problems about the density of reductions such as the conjecture of Joshi-Rajan, and the generalization of the conjecture of Serre. In this paper, we prove…

We develop the theory of geometric Eisenstein series and constant term functors for $\ell$-adic sheaves on stacks of bundles on the Fargues-Fontaine curve. In particular, we prove essentially optimal finiteness theorems for these functors,…

This is the second installment of an exposition of an ACL2 formalization of finite group theory. The first, which was presented at the 2022 ACL2 workshop, covered groups and subgroups, cosets, normal subgroups, and quotient groups,…

Classical results of Milnor, Wood, Mather, and Thurston produce flat connections in surprising places. The Milnor-Wood inequality is for circle bundles over surfaces, whereas the Mather-Thurston Theorem is about cobording general manifold…