Related papers: Potpourri, 2
Open issues on the structure of multiple interactions are outlined. An improved model is summarized, with a new approach to correlated parton densities in flavour, colour, longitudinal and transverse momenta, for both hard-scattering…
The purpose of this talk is to address a couple of simple-sounding questions: what boundary conditions are compatible with (a) Classical integrability? (b) Quantum integrability?
In this part, we prove several quantitative results concerning with the Szego minimum problem for classes of measure on the unit circle concentrated on small subsets. As a by-product, we refute one conjecture of Nevai. This note can be read…
These are the lecture notes for an introductory course on black holes and some aspects of their interaction with the classical and quantum world. The focus is on phenomena of "fundamental physics" in the immediate surroundings of the black…
We show how our recent results on compositions of d.c. functions (and mappings) imply positive results on extensions of d.c. functions (and mappings). Examples answering two natural relevant questions are presented. Two further theorems,…
Two types of Poisson pencils connected to classical R-matrices and their quantum counterparts are considered. A representation theory of the quantum algebras related to some symmetric orbits in $sl(n)^*$ is constructed. A twisted version of…
In earlier work we initiated a program to study relationships between finite groups and arithmetic geometric invariants of modular curves in a systematic way. In the present work we continue this program, with a focus on the two smallest…
This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.
We show that, in toric manifolds, one can characterize the sign of the Ricci curvature in terms of the convexity of the volume functional. More generally we discuss relationships between (i) Ricci curvature and volume, (ii) totally real and…
We discuss a number of open problems about mapping class groups of surfaces. In particular, we discuss problems related to linearity, congruence subgroups, cohomology, pseudo-Anosov stretch factors, Torelli subgroups, and normal subgroups.
We present a discussion about the local isometric rigidity problem in codimension 2 with a concrete example. We show the necessity of extending the notions of genuine and honest rigidity in order to have the transitivity property. In order…
These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system…
The aim of this note is: (a) to propose a generalization of tetrahedron equations from \cite{S} and of their solutions. Due to appearance of a larger number of parameters the $R$-matrices from \cite{S} will be replaced by…
The aim of the work is to construct new polynomial systems, which are solutions to certain functional equations which generalize the second-order differential equations satisfied by the so called classical orthogonal polynomial families of…
The present note sketches a theory of constructs.
This review article is the second part of the project ``Selected Topics of Social Physics". The first part has been devoted to equilibrium systems. The present part considers nonequilibrium systems. The style of the paper combines the…
These notes provide an elementary (and incomplete) sketch of the objects and ideas involved in monstrous and umbral moonshine. They were the basis for a plenary lecture at the 18th International Congress on Mathematical Physics, and for a…
This note is the follow up to a paper by M. Waldschmidt.
We consider the moduli space of bordered Riemann surfaces with boundary and marked points. Such spaces appear in open-closed string theory, particularly with respect to holomorphic curves with Lagrangian submanifolds. We consider a…
These Course Notes provide an introduction to mathematical proofs for undergraduate students transitioning from computational calculus to abstract mathematics. Topics include propositional logic, proof techniques, mathematical induction,…