References for Edward's mini course:
A great introduction to RMT and many of the things we saw in both lectures: https://www.lpthe.jussieu.fr/~zuber/RMT_2012.pdf
- The "Planar Diagrams" paper, which also does the quartic matrix integral I used as the main example for the 't Hooft expansion (their g is already the 't Hooft coupling): https://projecteuclid.org/journalArticle/Download?urlId=cmp%2F1103901558 . The answer to the two exercises I gave can be found in Eqs. 18 (for the large N interacting eigenvalue distribution, which matches the Monte-Carlo simulation we showed in class) and 21f and Tabel 1 which computes the free energy of the matrix model at large N (but to all orders in the 't Hooft coupling), using Eq. 10.
- The seminal paper by 't Hooft: https://webspace.science.uu.nl/~hooft101/gthpub/planar_diagram_theory.pdf
- A discussion of the variables that become classical at large N, also known as the large N masterfield. The paper I mentioned by Gopakumar & Gross, "Mastering the Masterfield": https://arxiv.org/pdf/hep-th/9411021
References for Elise's mini-course
- Multiple zeta values: from numbers to motives a now classic text by Fresan and Gil going deep into algebraic geometry. Chapter 1 is however very accessible.
- Feynman integrals and hyperlogarithms: Erik Panzer's PhD thesis, with a very detailed exposition of parametric Feynman integrals.
- Feynman Integrals by S. Weinzierl: Additional very complete resource for Feynman integrals with a long section on the graph polynomials.
- Proof of the Zig Zag conjecture by F.Brown and O.Schnetz
- Proofs of $\zeta(2)= \frac{\pi^2}{6}$
- Proof of irrationality of $\zeta(3)$ by Beukers
- Feynman integrals and hyperlogarithms: Erik Panzer's PhD thesis, with a very detailed exposition of parametric Feynman integrals.
- Feynman Integrals by S. Weinzierl: Additional very complete resource for Feynman integrals with a long section on the graph polynomials.
- Proof of the Zig Zag conjecture by F.Brown and O.Schnetz
- Proofs of $\zeta(2)= \frac{\pi^2}{6}$
- Proof of irrationality of $\zeta(3)$ by Beukers
