Self Learning - Moonshine beyond the Monster

Question

EDIT: I tried to introduce some of the parts that I could use extra reading in the below list, and changed the final question to be more specific to the list.

I am working on a individual study as an undergraduate, and my topic of interest is about number theory and physics, and in particular the following book Moonshine beyond the Monster attracted me and was advised me the most. The thing is , even though I have undergraduate level understanding of algebra, Galois theory, complex analysis and real analysis, along with a bit higher level topology (Munkres) and differential geometry (Lee's) background, I think some supplementary material along this book would be very helpful. More specifically, a course related to this subject would be very helpful.

This book contains subjects as :

• Modular forms

• Kac-Moody algebras
• CFT and TQFT
• Vertex Operator algebras

What would be some supplemental resources for subjects listed above from this book?

Answer 1

I think you have bitten off more than you can chew, let alone digest. That said, this might help: https://wstein.org/edu/2010/414/projects/padvorac.pdf

Introduction

As noted in the abstract, the end motivation here, in simple, is to develop the definitions needed to actually understand the very peculiar key observation that brought about “moonshine” theory, a recent development interweaving number theory, algebra, and to a lesser extent, physics. By taking this admittedly very shallow approach to introducing modular forms, it is sure that a large portion of their depth will be lost; as an undergraduate research project, this is nearly bound to happen regardless, as many needed ideas are in the toolboxes of graduate algebra. That is the downside of what I’ll be presenting here. The upshot is that it will be an undergraduate-accessible introduction to these topics, and a small glimpse into the motivation of the Monstrous Moonshine theory and conjectures.