Related papers: Selected papers
Fusion frames are a very active area of research today because of their myriad of applications in pure mathematics, applied mathematics, engineering, medicine, signal and image processing and much more. They provide a great flexibility for…
We give some remarks on twisted determinant line bundles and Chern-Simons topological invariants associated with real hyperbolic manifolds. Index of a twisted Dirac operator is derived. We discuss briefly application of obtained results in…
This is an extended version of my 2018 Heinemann prize lecture describing the work for which I got the prize. The citation is very broad so this describes virtually all my work prior to 1995 and some afterwards. It discusses work in…
In this paper, we study the integral curvatures of Finsler manifolds and prove several Myers type theorems.
Plan of this report is given below: 1. Motivation from Physical and Mathematical Point of View; 2. Differential Calculi on Finite Groups; 3. Metrics; 4. Lagrangian Field Theory and Symplectic Structure; 5. Scalar Field Theory and Spectral…
This manuscript describes in some detail the basic features of higher-spin gauge fields. After presenting some introductory material, I turn to the different formulations available at the free level and finally end with a discussion of the…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
This paper is a self-contained presentation of certain aspects of the theory of weighted Sobolev spaces and elliptic operators on non-compact Riemannian manifolds. Specifically, we discuss (i) the standard and weighted Sobolev Embedding…
We review some selected recent results concerning selection principles in topology and their relations with several topological constructions.
After a rapid introduction to the physical motivations and a succinct presentation of heuristic results, this survey summarises the main mathematical results known on the Edwards-Anderson and the Sherrington-Kirkpatrick models of spin…
Throughout John Wheeler's career, he wrestled with big issues like the fundamental length, the black hole and the unification of quantum mechanics and relativity. In this essay, I argue that solid state physics -- historically the study of…
We consider the class of profinite diffeological spaces, that is, diffeological spaces which diffeologies are deduced by pull-back of diffeologies on finite-dimensional manifolds through a system of projection mappings. This class includes…
Affine metrics and its associated algebroid bundle are developed. Theses structures are applied to the general relativity and provide an structure for unification of gravity and electromagnetism. The final result is a field equation on the…
This entry contains the core material of my habilitation thesis, soon to be officially submitted. It provides a self-contained presentation of the original results in this thesis, in addition to their detailed proofs. The motivation of…
This is mostly* a non-technical exposition of the joint work arXiv:1212.0373 with Caporaso and Payne. Topics include: Moduli of Riemann surfaces / algebraic curves; Deligne-Mumford compactification; Dual graphs and the combinatorics of the…
We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, algebraic statistics, integrable systems, configuration…
By using a certain second order differential equation, the notion of adapted coordinates on Finsler manifolds is defined and some classifications of complete Finsler manifolds are found. Some examples of Finsler metrics, with positive…
We propose a graded classification of the entire field of multivector physics, including all alternative points of view. The (often tacit) postulates of different types of formulations are contrasted, summarizing their consequences.…
This paper has been withdrawn. It will be split into two separate papers. New results will be added in both papers.
From descent theory to higher geometry, the idea of gluing has been embedded in many elegant and powerful techniques, proving instrumental for the solution of many problems. In this paper, we introduce a framework that allows to link…