Related papers: The Schwarz Lemma: An Odyssey

Lecture notes of a master course given at Orsay between 2019-2024. Topics covered include Part I: One-dimensional random walks, cycle lemma and Bienaym\'e--Galton--Watson random trees. Part II: Erd\"os--R\'enyi random graphs, three proofs…

These lecture notes concern information-theoretic notions of entropy. They are intended for, and have been successfully taught to, undergraduate students interested inresearch careers. Besides basic notions of analysis related to…

A given question can be defined in terms of the set of statements or assertions that answer it. Application of logical inference to these sets of assertions allows one to derive the logic of inquiry among questions. There are interesting…

Selected examples of possible origins of power-law distributions are presented.

This is a non-standard paper, containing some problems, mainly in model theory, which I have, in various degrees, been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me,…

This short paper focuses on Schr\"oder's contribute towards a structural view of group theory.

I discuss some compelling suggestions about particles which could be the dark matter in the universe, with special attention to experimental searches for them.

Comments on extensions of Verma modules in the Bernstein-Gelfand-Gelfand Category O.

A general formulation of the basic conflict of the information problem is given, encapsulated in a "black hole theorem." This is framed in a more general context than the usual one of quantum field theory on a background, and is based on…

Collatz Conjecture sequences increase and decrease in seemingly random fashion. By identifying and analyzing the forms of numbers, we discover that Collatz sequences are governed by very specific, well-defined rules, which we call cascades.

In this paper, we define probabilistic n-Banach spaces along with some concepts in this field and study convergence in these spaces by some lemmas and theorem.

This article offers a gentle introduction to the axiom of choice. We introduce the axiom, discuss some common objections to it, and present three kinds of reasons to accept it. Although the exposition is aimed at non-experts in set theory,…

I present a brief theory overview of the CHARM-2015 conference.

We give a presentation of abelian class field theory.

This is a lecture notes for a mini-course in Department of Mathematics, Ghent University, 14 Mar.-25 Mar. 2023.

This note points out that the assertions of [1] are groundless and incorrect.

This is a survey on the ongoing development of a descriptive theory of represented spaces, which is intended as an extension of both classical and effective descriptive set theory to deal with both sets and functions between represented…

This is a set of lecture notes that developed out of courses on the lambda calculus that I taught at the University of Ottawa in 2001 and at Dalhousie University in 2007 and 2013. Topics covered in these notes include the untyped lambda…

The conjecture about the Orlicz P\'olya-Szeg\"o principle posed in [43] is proved. The cases of equality are characterized in the affine Orlicz P\'olya-Szeg\"o principle with respect to Steiner symmetrization and Schwarz spherical…

The note complements topological aspects of the theory of chiral algebras.