相关论文: What is moonshine?

This is an extended abstract for a survey talk given in Oberwolfach on 1st December 2022, slightly updated in June 2023. I survey some work around the notion of quasiminimality and some of the progress towards Zilber's conjecture from the…

A basic family of solenoids is discussed, especially from the point of view of analysis on metric spaces.

This short note is an "elementary'' introduction to the conjectural theory of motives.

In this short note we improve the best to date bound in Godbersen's conjecture, and show some implications for unbalanced difference bodies.

We determine the space of 1-point correlation functions associated with the Moonshine module: they are precisely those modular forms of non-negative integral weight which are holomorphic in the upper half plane, have a pole of order at most…

We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.

In this short survey article, we aim to provide an up to date information on the progress made towards Schurs exponent conjecture and related conjectures. We also mention the connection between Schurs exponent conjecture and Noether's…

These lecture notes describe the current state of affairs for Manin's conjecture in the context of del Pezzo surfaces.

An account of the subjective elements of quantum mechanics or of whether, as Einstein famously asked, the Moon exists when nobody is looking at it.

We discuss some easy statements dealing with linear inhomogeneous Diophantine approximation. Surprisingly, we did not find some of them in the literature.

This is an introduction to Taubes's proof of the Weinstein conjecture, written for the AMS Current Events Bulletin. It is intended to be accessible to nonspecialists, so much of the article is devoted to background and context.

We propose a moonshine for the sporadic Mathieu group M_12 that relates its conjugacy classes to various modular forms and Borcherds Kac-Moody Lie superalgebras.

This is an overview and a preview of the theory of "mixed motives of level 1" explaining some results, projects, ideas and indicating a bunch of problems.

The article provides a counterexample to a conjecture by Blocki-Zwonek.

The goal of this article is to invite the reader to get to know and to get involved into higher Teichm\"uller theory by describing some of its many facets.

We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.

We expand upon some topics reviewed and sketched in a book to appear with more details, embellishments, and some new material of a speculative nature.

Presented here are over one hundred conjectures ranging from easy to difficult, from many mathematical fields. I also summarize briefly methods and tools that have led to this collection.

We are interested in several informal statements referred as "Kontinuit\"atssatz" in the recent literature on analytic continuation. The basic (unstated) principle that seems to be in use in these works appears to be a folk theorem. We…

Fifty years on from the first detailed chemical kinetic modelling of astronomical sources, I provide some introductory comments on the history of astrochemistry, summarise some personal views on the topics covered in this discussion…