A Connection between K3 Surfaces and the Conway Moonshine Module Pubblico

Abstract

In this paper, we survey an interesting duality between K3 surfaces and the Conway moonshine modules via Jacobi forms. K3 surfaces are studied extensively in the context of string compactification since they are manageable, yet non-trivial kind of Calabi-Yau manifold. An important topological invariant discovered by Witten in [1] is the elliptic genus. The elliptic genus of a K3 surface is a weak modular form of weight zero and index 1. In this text we show that a certain graded trace associated to the Conway moonshine module coincides with the K3 elliptic genus.

Table of Contents

Section 1: Introduction…………………………………………………………………..1

Section 2: Background …………………………………………………………………..1

Section 3: Main Theorem………………………………………………………………14

Section 4: References……………………………………………………………………19

About this Honors Thesis

Rights statement

• Permission granted by the author to include this thesis or dissertation in this repository. All rights reserved by the author. Please contact the author for information regarding the reproduction and use of this thesis or dissertation.

School	Emory College
Department	Mathematics
Degree	B.S.
Submission	Honors Thesis
Language	English
Research Field	Mathematics
Parola chiave	Moonshine Conway Group K3 Surfaces
Committee Chair / Thesis Advisor	Duncan, John, Emory University
Committee Members	Zureick-Brown, David, Emory University Srivastava, Ajit, Emory University

Ultima modifica

Primary PDF

Thumbnail	Title	Date Uploaded	Actions
	A Connection between K3 Surfaces and the Conway Moonshine Module ()	2020-04-14 18:37:26 -0400	Press to Select an action Download

Supplemental Files

Thumbnail	Title	Date Uploaded	Actions