Related papers: Much Ado About Something: Why Lieb-Robinson bounds…
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…
Recent links between Finsler Geometry and the geometry of spacetimes are briefly revisited, and prospective ideas and results are explained. Special attention is paid to geometric problems with a direct motivation in Relativity and other…
The dynamics of binary pulsars can be used to test different aspects of gravitation. This is particularly important to constrain alternatives to general relativity in regimes which are not probed by other methods. In this short…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
A generalization of the classical Leibniz rule for the covariant derivative on a vector bundle is obtained.
We improve known upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and non-periodic settings. Some of our bounds are sharp up to logarithmic factors.
We give a Lieb-Robinson bound for the group velocity of a large class of discrete quantum systems which can be used to prove that a non-vanishing spectral gap implies exponential clustering in the ground state of such systems.
We review some recent results on eigenvalues of fractional Laplacians and fractional Schr\"odinger operators. We discuss, in particular, Lieb-Thirring inequalities and their generalizations, as well as semi-classical asymptotics.
The long history of the research concerning the possible existence of bound or resonant states in light multineutron systems, essentially $^3$n and $^4$n, is reviewed. Both the experimental and the theoretical points of view have been…
The covariant Klein-Gordon equation requires twice the boundary conditions of the Schrodinger equation and does not have an accepted single-particle interpretation. Instead of interpreting its solution as a probability wave determined by an…
LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial…
The Riemann-Roch theorem is of utmost importance in the algebraic geometric theory of compact Riemann surfaces. It tells us how many linearly independent meromorphic functions there are having certain restrictions on their poles. The aim of…
This document is an introduction to and review of two-dimensional mathematical physics. The reader is introduced to the subject matter primarily through problems, which are presented along with detailed worked solutions. For each chapter,…
When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like…
In this talk we consider the modifications induced by heavy physics on the triviality and vacuum stability bounds on the Higgs-boson mass. We parameterize the heavy interactions using an effective Lagrangian and find that the triviality…
This paper is concerned with complex macroscopic behaviour arising in many-body systems through the combinations of competitive interactions and disorder, even with simple ingredients at the microscopic level. It attempts to indicate and…
We give two generalizations of the Clifford theorem to algebraic surfaces. As an application, we obtain some bounds for the number of moduli of surfaces of general type.
Mathematical physics has many facets, of which we shall briefly give a (very partial) description, centered around those of main interest for Elliott and us (Moshe Flato and I). In our case these aspects had as a corollary a variety of…
A synthetic study of Pitman's and L\'evy's theorems for one-dimensional Brownian bridges with arbitrary endpoints is provided.
We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…