Mini-course on string amplitudes and automorphic forms at Durham

Marcus Berg, Spring 2020

This mini-course will discuss some particular topics in the calculation of amplitudes, with focus on loop amplitudes. These objects in physics are described by automorphic forms, like nonholomorphic Eisenstein series, most commonly for SL(2) but more recently for other Lie groups. I will focus on topics that are of common interest to physicists and mathematicians, including modular graph functions, threshold corrections/theta lifts and higher-genus amplitudes. The use of symbolic manipulation software, including Kasper Peeters's Cadabra, will be encouraged but not required.

Each lecture will be about 1.5 hours, with a short break. A few videos will complement lectures, in addition to my string videos. There will be three homework sets, where collaboration is encouraged (especially between mathematics and physics!)

Date Time Topics A few papers
Wed, May 6 10am Intro string amplitudes, open vs. closed, loops 1603.05262
Wed, May 6 1pm Intro automorphic forms: Eisenstein series, Maass forms 1407.0027, Appendix E
Fri, May 8 10am Holomorphy and Jacobi forms
Fri, May 8 1pm Physics talk (motivations) 1910.02745
Mon, May 11 10am Kronecker-Eisenstein series as Green's functions 1407.0027, Appendix E
Mon, May 11 1pm Assembling string amplitudes
Wed, May 13 10am Problem session

Homework Set 1

PDF. Handed out: Wed, May 6. Due: Wed, May 13.

Homework Set 2

PDF. Handed out: Wed, May 13. Hand in: Wed, May 27.


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