Related papers: Math{\'e}matiques, musique et cosmologie : A parti…
This talk reviews the proposal for dynamically selecting the most probable wavefunction of the universe propagating on the landscape of string theory, by means of quantum cosmology. Talk given at 'Albert Einstein Century International…
A cosmological description of the universe is proposed in the context of Hamiltonian formulation of a Bianchi IX cosmology minimally coupled to a massless scalar field. The classical and quantum results are studied with special attention to…
Discussion of "Instrumental Variables: An Econometrician's Perspective" by Guido W. Imbens [arXiv:1410.0163].
Examples are presented of applications of the Lema\^{i}tre - Tolman model to problems of astrophysics and gravitation theory. They are: 1. Inferring the spatial distribution of matter by interpretation of observations; 2. Interaction of…
We discuss new approaches to fundamental problems of mathematics and mathematical physics such as mathematical foundation of quantum field theory, the Riemann hypothesis, and construction of noncommutative algebraic geometry.
One hundred years ago, Hilbert gave a list of important open problems in mathematics. His 15th problem asked for the development of a rigorous calculus explaining Schubert's enumerative results for intersecting varieties defined by rank…
This essay inquires how mathematical beings could be inserted into the architecture of modes of existence proposed by Bruno Latour in the framework of his pluralist and renewed ontology of the modern world. After a description of the…
In his essay "Nature Conformable to Herself" the late Murray Gell-Mann expands on an observation of Newton that theories of seemingly disparate phenomena in the universe often make use of similar ideas and similar mathematical structure.…
Contents: Introduction. The Present State of the Universe. What Can We Expect From a Complete Cosmological Theory? An Overview of Quantum Effects in Cosmology. Parametric (Superadiabatic) Amplification of Classical Waves. Graviton Creation…
In this paper, we obtain a complete characterization for the compact difference of two composition operators acting on Bergman spaces with weight $\omega=e^{-\eta}$, $\Delta\eta>0$ in terms of the $\eta$-derived pseudodistance of two…
This is the pdf -version of the author's Ph.D. thesis (1995, ULB, Belgium). The notion of symeplectic symmertic space is introduced and studied via Lie theoretical and symplectic geoemetrical methods. The first chapter concerns basic…
The Compositional Integral is defined, formally constructed, and discussed. A direct generalization of Riemann's construction of the integral; it is intended as an alternative way of looking at First Order Differential Equations. This brief…
This set of lecture notes gives an introduction to holomorphic function spaces as used in mathematical physics. The emphasis is on the Segal-Bargmann space and the canonical commutation relations. Later sections describe more advanced…
This paper presents the first comprehensive systematic review of literature on style-based composer identification and authorship attribution in symbolic music scores. Addressing the critical need for improved reliability and…
In order to account for the observable Universe, any comprehensive theory or model of cosmology must draw from many disciplines of physics, including gauge theories of strong and weak interactions, the hydrodynamics and microphysics of…
In the article "The Tale of Two Queens and Two Towering Figures" published in CNJ in 2012 (CNJ vol. 57 No. 5, pp. 304-315), we discussed the contributions of Copernicus and Newton to coin minting and monetary reforms, as well as the…
I discuss the historical and conceptual roots of reasoning about the parameters of fundamental physics and cosmology based on selection effects. I argue concretely that such reasoning can and should be combined with arguments based on…
We show that the cosmological large number coincidence can be interpreted as giving the filling factor in a Landau problem. The analogy with the Landau problem leads naturally to the noncommutativity of the gravitational and matter degrees…
This paper is devoted to certain applications of classical Whitney decomposition of the upper half space R^n+1 to various problems in harmonic function spaces in the upper half space.We obtain sharp new assertions on embeddings,distances…
In this tutorial, we provide an overview of many of the established combinatorial and algebraic tools of Schubert calculus, the modern area of enumerative geometry that encapsulates a wide variety of topics involving intersections of linear…