Related papers: Local and global Langlands conjecture(s) over func…
We establish endoscopic and stable trace formulas whose discrete spectral terms are weighted by automorphic $L$-functions, by the use of basic functions that are incorporated into the global spectral and geometric coefficients. This is a…
The Intelligent Fault Diagnosis of rotating machinery currently proposes some captivating challenges. Although results achieved by artificial intelligence and deep learning constantly improve, this field is characterized by several open…
I give a simple general prescription for computing the spectral functions of local operators in the Tomonaga-Luttinger model from the space-time correlation functions. The method is significantly simpler than directly transforming the…
We study topological defects with a general structure in higher-dimensional cosmological backgrounds described by a set of angle deficit parameters. As special cases, they include higher-dimensional generalizations of cosmic strings and…
Parametrized field theories, which are generally covariant versions of ordinary field theories, are studied from the point of view of the covariant phase space: the space of solutions of the field equations equipped with a canonical…
Let $G$ be a locally compact abelian topological group. For locally bounded measurable functions $\varphi: G\to\Bbb {C}$ we discuss notions of spectra for $\varphi$ relative to subalgebras of $L^{1}(G)$. In particular we study polynomials…
We devise a new criterion for linear independence over function fields. Using this tool in the setting of dual t-motives, we find that all algebraic relations among special values of the geometric function field Gamma-function are explained…
The framework of locally covariant quantum field theory is discussed, motivated in part using "ignorance principles". It is shown how theories can be represented by suitable functors, so that physical equivalence of theories may be…
The goal of this paper is to give a simple proof of Deligne's conjecture (proven by Fujiwara) and to generalize it to the situation appearing in our joint project with David Kazhdan on the global Langlands correspondence over function…
We discuss properties of random fractals by means of a set of numbers that characterize their universal properties. This set is the generalized singularity specturm that consists of the usual spectrum of mulitfractal dimensions and the…
Geometric symmetry induces symmetries of function spaces, and the latter yields a clue to global analysis via representation theory. In this note we summarize recent developments on the general theory about how geometric conditions affect…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
In this article, using the language of jet space, we propose a functional class space for pseudo-local functionals. We test this functional class proposal in a number of examples ranging from string-field-theory to AdS/CFT dualities.…
On a reasonable class of domains in $\CC^n$, we characterize those holomorphic functions which continue analytically past the boundary. Then we give some applications of this result to holomorphic mappings. In addition, some new results…
The aim of this paper is to construct and examine three candidates for local-to-global spectral sequences for the cohomology of diagrams of algebras with directed indexing. In each case, the $E^2$ -terms can be viewed as a type of local…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
We develop a holomorphic functional calculus for (multivalued linear) operators on locally convex vector spaces. This includes the case of fractional powers along Lipschitz curves.
In this article, we consider the links between parabolic induction and the local Langlands correspondence. We enunciate a conjecture about the (enhanced) Langlands parameters of supercuspidal representation of split reductives $p$-adics…
We generalize the position- and momentum-space entanglement cuts to a family of cuts corresponding to regions in the classical phase space. We explicitly compute the entanglement spectra of free fermionic many-body wavefunctions for a…
New geometric structures that relate the lagrangian and hamiltonian formalisms defined upon a singular lagrangian are presented. Several vector fields are constructed in velocity space that give new and precise answers to several topics…