Related papers: What is moonshine?

In this short note we present a class of conjectures on partitions of integers as summations of primes, which are extensions of Goldbach conjecture.

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…

The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…

On March 19-21, 1998, a workshop devoted to questions of the pomeron and the odderon in high energy scattering was held in Heidelberg. This note gives a personal account of some of the issues discussed at this workshop. Of course,…

A conjecture about the quantum nature of classical probabilites is set forth and discussed.

This rough note describes some attempts to define a notion of enriched topology (and the associated theory of enriched stacks) on a category enriched over a symmetric monoidal model category, and poses some related questions.

W. M. Hirsch formulated a beautiful conjecture on diameters of convex polyhedra.I suggest a new viewpoint with the deformation and moduli of polytopes.

These are the notes from my courses on the arithmetic of quadratic forms.

These lecture notes are based on a set of six lectures that I gave in Edinburgh in 2008/2009 and they cover some topics in the interface between Geometry and Physics. They involve some unsolved problems and conjectures and I hope they may…

An out of the box intellectual path exploring the foundations of quantum mechanics is discussed in some detail, in order to clarify why a possibly different way to look at the relevant fundamental questions can be identified and can support…

We discuss the connection between the smooth and metric structure on quotient spaces, prove smoothness of isometries in special cases and discuss an application to a conjecture of Molino.

This is a list of some problems and conjectures related to various types of algebras, that is to algebraic operads. Some comments and hints are included.

The search for dark matter is a very wide and active field of research. Many potential hints of dark matter have appeared recently which led to a burst of theoretical activity and model building. I necessarily concentrate here only in some…

Twenty-five years ago, Conway and Norton published their remarkable paper `Monstrous Moonshine', proposing a completely unexpected relationship between finite simple groups and modular functions. This paper reviews the progress made in…

We report the results of our empirical investigations on the Bateman-Horn conjecture. This conjecture, in its commonly known form, produces rather large deviations when the polynomials involved are not monic. We propose a modified version…

The Frankl conjecture (called also union-closed sets conjecture) is one of the famous unsolved conjectures in combinatorics of finite sets. In this short note, we introduce and to some extent justify some variants of the Frankl conjecture.

This brief note, written for non-specialists, aims at drawing an introductive overview of the multiverse issue.

These informal notes deal with a number of questions related to sums and integrals in analysis.

Lecture notes on selected topics in the theory of gravitation.

This is a short discussion of the definition of monad which was given by G.W. Leibniz in his "Monadology."