相关论文: What is moonshine?

Ce texte est une d\'emontration compl\`ete de la conjecture de Catalan \'elabor\' ee \`a la suite d'un s\'eminaire fait \`a Lausanne entre 2002 et 2004, juste apr\`es l'annonce de la merveilleuse preuve de Preda Mihailescu

In an automatic search, we found conjectural recurrences for some sequences in the OEIS that were not previously recognized as being D-finite. In some cases, we are able to prove the conjectured recurrence. In some cases, we are not able to…

I use an instrumental approach to investigate some commonly made claims about interpretations of quantum mechanics, especially those that pertain questions of locality. The here presented investigation builds on a recently proposed taxonomy…

The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…

This is a survey talk on the study of Gel'fand-Dorfman bialgebras.

These are yet another lecture notes on Seiberg-Witten invariants, where no claim of originality is made, they contain a discussion of some related results from the recent literature.

This is an extension and background to a talk I gave on 9 October 2013 to the Brown Graduate Student Seminar, called `A friendly intro to sieves with a look towards recent progress on the twin primes conjecture.' During the talk, I mention…

We consider the situation in which a finite group acts on an infinite-dimensional graded module in such a way that the graded trace functions are weakly holomorphic modular forms. Under a mild hypothesis we completely describe the…

In this paper we present some observations about the well-known Goldbach conjecture. In particular we list and interpret some numerical results which allow us to formulate a relation between prime numbers and even integers. We can also…

These are lecture notes written at the University of Zurich during spring 2014 and spring 2015. The first part of the notes gives an introduction to probability theory. It explains the notion of random events and random variables,…

We exposit the construction of Rademacher sums in arbitrary weights and describe their relationship to mock modular forms. We introduce the notion of Rademacher series and describe several applications, including the determination of…

These informal notes are concerned with sums and averages in various situations in analysis.

In this work we resolve several conjectures stated in the On-Line Encyclopedia of Integer sequences.

In this paper, a theory of quandle rings is proposed for quandles analogous to the classical theory of group rings for groups, and interconnections between quandles and associated quandle rings are explored.

The goal of this paper is to introduce Hodge 1-motives of algebraic varieties and to state a corresponding cohomological Grothendieck-Hodge conjecture, generalizing the classical Hodge conjecture to arbitrarily singular proper schemes.

We show how a commutative monad gives rise to a theory of extensive quantities, including (under suitable further conditions) a differential calculus of such. The relationship to Schwartz distributions is dicussed. The paper is a companion…

The aim of this survey article is to highlight several notoriously intractable problems about knots and links, as well as to provide a brief discussion of what is known about them.

I offer a brief summary, with commentary, of theoretical contributions to Moriond QCD 2008.

A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…

This article gives a brief survey of the theory and applications of anomalies.