Related papers: On interactions between harmonic analysis and the …
The aim of the present survey paper is to provide an accessible introduction to a new chapter of representation theory - harmonic analysis for noncommutative groups with infinite-dimensional dual space. I omitted detailed proofs but tried…
Harmonic maps are nonlinear extensions of harmonic functions. They are critical points of natural energy functionals between Riemannian manifolds. Such type of problems appear in Physics, Geometry of Finance and the study of regularity and…
We study a generalization of the classical correspondence between homogeneous quadratic polynomials, quadratic forms, and symmetric/alternating bilinear forms to forms in $n$ variables. The main tool is combinatorial polarization, and the…
We study in this paper some connections between the Fraisse theory of amalgamation classes and ultrahomogeneous structures, Ramsey theory, and topological dynamics of automorphism groups of countable structures.
Fourier Transforms is a first in a series of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such…
The purpose of this article is to survey certain aspects of multilinear harmonic analysis related to notions of transversality. Particular emphasis will be placed on the multilinear restriction theory for the euclidean Fourier transform,…
Aspects of the theory of characteristic modes, based on their variational formulation, are presented and an explicit form of a related functional, involving only currents in a spatial domain, is derived. The new formulation leads to deeper…
This is a survey of recent progress in several areas of combinatorial algebra. We consider combinatorial problems about free groups, polynomial algebras, free associative and Lie algebras. Our main idea is to study automorphisms and, more…
A general framework of constructions of endoscopy correspondences via automorphic integral transforms for classical groups is formulated in terms of the Arthur classification of the discrete spectrum of square-integrable automorphic forms.…
We introduce the natural notion of (p,q)-harmonic morphisms between Riemannian manifolds. This unifies several theories that have been studied during the last decades. We then study the special case when the maps involved are…
We consider spaces for which there is a notion of harmonicity for complex valued functions defined on them. For instance, this is the case of Riemannian manifolds on one hand, and (metric) graphs on the other hand. We observe that it is…
A study of harmonic maps into Lie groups as a generalisation of the study of other well-known integrable systems, particularly the Toda and self-dual Chern Simons theories.
We give archimedean and non-archimedean constructions of Darmon points on modular abelian varieties attached to automorphic forms over arbitrary number fields and possibly non-trivial central character. An effort is made to present a…
We will review the main results concerning the automorphism groups of saturated structures which were obtained during the two last decades. The main themes are: the small index property in the countable and uncountable cases; the…
The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the second in a series of papers in…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
Noncommutative harmonic analysis is used to solve a nonparametric estimation problem stated in terms of compound Poisson processes on compact Lie groups. This problem of decompounding is a generalization of a similar classical problem. The…
We study the automorphism groups of finite-dimensional cyclic Leibniz algebras. In this connection, we consider the relationships between groups, modules over associative rings and Leibniz algebras.
This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…
In this work, we establish a relationship between the sum of irreducible character degrees and the number of twisted involutions associated with the automorphisms of a finite group. We develop algorithmic frameworks for evaluating these…