Reading Seminar - Feynman Integrals and Moduli Spaces WS 2022/23

Reading Seminar - Feynman Integrals and Moduli Spaces WS 2022/23

Organizer: Daniele Agostini.

Time: Friday, 9:00

Place: On Zoom. The link is here.



The aim of this reading group is to understand the connection between Feynman integrals and amplitudes on one side and algebraic geometry, tropical geometry and D-modules on the other. These connections have appeared recently in different fields, such as enumerative geometry of real and complex curves, topology of moduli spaces of curves or numerical evaluations of Feynman integrals.

References : At the beginning, we will be inspired by the paper:

Depending on time, we might continue in different directions such as: Other useful references:

Lectures and notes

  1. 04.11.2022, Daniele: Introduction, Feynman diagrams, Feynman integrals. Notes.
  2. 11.11.2022, Claudia and Dmitrii: Graph polynomials, trees and forests. Laplacian, deletion and contraction (Weinzierl, Chapter 3). Notes Claudia, Notes Dmitrii.
  3. 18.11.2022, Javier: Riemann surfaces, stable curves and their moduli spaces. Examples in genus zero and one. Notes.
  4. 25.11.2022, Lou-Jean: Tropical curves, linear systems and theta characteristics. Notes.
  5. 02.12.2022, Daniele: Theta functions, abelian varieties and their moduli spaces. Jacobians, the Torelli map and the Schottky problem. Notes.
  6. 09.12.2022, Victoria: Moduli spaces of tropical curves and tropical abelian varieties, the tropical Torelli map, and tropicalization. Notes.
  7. 2023, Speaker: Classical and tropical prime form. Amplitudes.
  8. 2023, Speaker: Amplitudes in the tropical limit.