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The Case of a Normal Subgroup
In this section we consider triples of the form (G, N, θ) in the particular case when the subgroup N ≤ G is normal.
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On Double Coset Decompositions of Real Reductive Groups for Reductive Absolutely Spherical Subgroups
The aim of this article is to show an induction argument to obtain the double coset decomposition...
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The Conjugacy Stability Problem for Parabolic Subgroups in Artin Groups
Given an Artin group A and a parabolic subgroup P , we study if every two elements of P that are conjugate in A , are also conjugate in P . We provide...
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An Exploration of Locally Spherical Regular Hypertopes
Hypertope is a generalization of the concept of polytope, which in turn generalizes the concept of a map and hypermap, to higher rank objects....
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Polyhedral Preliminaries
This chapter deals with cell complexes (also called “polyhedra”) with metrics of piecewise constant curvature. In other words, each cell is required...
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Spherical spectral synthesis on hypergroups
We introduce the basic concepts of spherical spectral synthesis on hypergroups, following the ideas of our paper [11]. The commutativity of...
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Homogeneous Coherent Configurations from Spherical Buildings and Other Edge-Coloured Graphs
We study a class of edge-coloured graphs, including the chamber systems of buildings and other geometries such as affine planes, from which we build...
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Saturn ring defect around a spherical particle immersed in a nematic liquid crystal
We consider a nematic liquid crystal occupying the three-dimensional domain in the exterior of a spherical colloid particle. The nematic is subject...
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The Ring of Conditions for Horospherical Homogeneous Spaces
These are notes of a five talks lecture series during the “Graduate Summer School in Algebraic Group Actions”, at McMaster University, June...
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Concentration estimates for finite expansions of spherical harmonics on two-point homogeneous spaces via the large sieve principle
We study the concentration problem on compact two-point homogeneous spaces for finite expansions of eigenfunctions of the Laplace–Beltrami operator...
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The modular Weyl–Kac character formula
We classify and explicitly construct the irreducible graded representations of anti-spherical Hecke categories which are concentrated one degree....
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Morse Theory and Bestvina–Brady Groups
Section 7.1 develops “Morse theory” for real-valued functions on convex cell complexes. There are two purposes: (1) to study finiteness properties of...
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Exhaustion functions and normal forms for proper maps of balls
We study a relationship between rational proper maps of balls in different dimensions and strongly plurisubharmonic exhaustion functions of the unit...
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Existence results for closed Finsler geodesics via spherical complexities
We apply topological methods and a Lusternik-Schnirelmann-type approach to prove existence results for closed geodesics of Finsler metrics on spheres...
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The Yau–Tian–Donaldson Conjecture for Cohomogeneity One Manifolds
We prove the Yau–Tian–Donaldson conjecture for cohomogeneity one manifolds, that is, for projective manifolds equipped with a holomorphic action of a...
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Momentum polytopes of projective spherical varieties and related Kähler geometry
We apply the combinatorial theory of spherical varieties to characterize the momentum polytopes of polarized projective spherical varieties. This...
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Aperiodic order and spherical diffraction, II: translation bounded measures on homogeneous spaces
We study the auto-correlation measures of invariant random point processes in the hyperbolic plane which arise from various classes of aperiodic...
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Weyl’s law for arbitrary archimedean type
We generalize the work of Lindenstrauss and Venkatesh establishing Weyl’s Law for cusp forms from the spherical spectrum to arbitrary archimedean...