Related papers: Elementary introduction to Moonshine
The word moonshine refers to unexpected relations between the two distinct mathematical structures: finite group representations and modular objects. It is believed that the key to understanding moonshine is through physical theories with…
This article is a short and elementary introduction to the monstrous moonshine aiming to be as accessible as possible. I first review the classification of finite simple groups out of which the monster naturally arises, and features of the…
In these notes, based on lectures given in Istanbul, we give an introduction both to Monstrous Moonshine and to the classification of rational conformal field theories, using this as an excuse to explore several related structures and go on…
We present a brief overview of Moonshine with an emphasis on connections to physics. Moonshine collectively refers to a set of phenomena connecting group theory, analytic number theory, and vertex operator algebras or conformal field…
These notes stem from lectures given by the first author (JM) at the 2008 "Moonshine Conference in Kashiwa" and contain a number of new perspectives and observations on Monstrous Moonshine. Because many new points have not appeared anywhere…
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…
As Mathieu moonshine is a special case of umbral moonshine, Thompson moonshine (in half-integral weight) is a special case of a family of similar relationships between finite groups and vector-valued modular forms of a certain kind. We call…
This is an informal write up of my talk in Berlin. It gives some background to Goddard's talk (math.QA/9808136) about the moonshine conjectures.
Lecture notes for an introductory course in elementary particles.
This is an introduction to the basic elements needed for the measurements and interpretation of data in the millimeter and sub-mm wavelength range. A more complete version will be published in the proceedings of the Saas Fee Winter School…
This is a short summary of my lectures given at the Fourth Mexican School on Gravitation and Mathematical Physics. These lectures gave a brief introduction to black holes in string theory, in which I primarily focussed on describing some of…
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…
I first recall the last occasion of meeting the late Professor Yoichiro Nambu in a hospital in Osaka. I then present a brief introduction to the moonshine phenomenon in string theory which is under recent investigations.
Umbral moonshine describes an unexpected relation between 23 finite groups arising from lattice symmetries and special mock modular forms. It includes the Mathieu moonshine as a special case and can itself be viewed as an example of the…
These notes on string theory are based on a series of talks I gave during my graduate studies. As the talks, this introductory essay is intended for young students and non-string theory physicists.
This is the written version of a set of introductory lectures on string theory.
This short note is an "elementary'' introduction to the conjectural theory of motives.
This set of Montreal lectures is an elementary and sketchy introduction to the general field of random matrices. The first half is devoted to combinatorial models, whereas the second half deals with random matrix questions(GUE, etc...).
With a jocund air, we present an observation on the first 24 coefficients of the modular invariant and of the modular discriminant. The observation is purely for the sake of entertainment and could be of some diversion to a mathematical…
These are the lecture notes of the introductory String Theory course held by one of the authors for the master program of Theoretical Physics at Turin University. The world-sheet approach to String Theory is pedagogically introduced in the…