Elliptic multiple zeta values, modular graph functions and genus 1 superstring scattering amplitudes

TL;DR

This thesis explores elliptic analogues of multiple zeta values and modular graph functions, which are crucial in computing genus one superstring amplitudes, providing new asymptotic results and insights into their structure.

Contribution

It introduces new asymptotic expansions for elliptic multiple zeta values and modular graph functions, enhancing the understanding of genus one superstring scattering amplitudes.

Findings

Derived explicit asymptotic expansions for elliptic functions

Identified analogies between genus zero and genus one amplitudes

Facilitated computations of superstring amplitudes at genus one

Abstract

In this PhD thesis we study holomorphic and non-holomorphic elliptic analogues of multiple zeta values, namely elliptic multiple zeta values and modular graph functions. Both classes of functions have been discovered very recently, and are involved in the computation of genus one superstring amplitudes. In particular, we obtain new results on the asymptotic expansion of these functions that allow us to perform explicit computations and point out analogies between genus zero and genus one amplitudes.