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|
Handed out: Wed, May 6. Due: Wed, May 13.
PDF. Handed out: Wed, May 13. Hand in: Wed, May 27.