DescriptionConnections between string theory, modular forms and number theory have been a topic of intense research in theoretical physics and mathematics for several decades. This project aims to explore these connections and their implications for our understanding of the fundamental laws of the universe.String theory is a theoretical framework that seeks to unify the laws of general relativity and quantum mechanics, while modular forms are mathematical functions with interesting properties related to symmetries and number theory. This project will investigate the ways in which string theory and modular forms are connected. Specifically, it will explore how certain types of modular forms appear naturally in the mathematics of string theory, and how these modular forms can be used to extract physical information about the theory. Depending on the student's interests, the project can be aimed towards more mathematical directions, e.g. understanding the theory of classical holomorphic and non-holomorphic Eisenstein series and the theory of Maass forms thus connecting with some elements of number theory like multiple zeta values. While for more physics inclined students, the project could be directed towards the study of particular modular functions arising in string theory calculations, like partition functions or modular graph functions and their connections with the world of multiple zeta values.
PrerequisitesComplex Analysis.Co-requisites (Not necessary but useful)Superstrings IV.ResourcesYou can look up the lecture notes by Eric D'Hoker and Justin Kaidi Lectures on modular forms and strings.Relevant books for the more ''maths inclined'' students include the following:
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