The ESI program Amplitudes and Algebraic Geometry aims to develop new mathematical paradigms for the fundamental interactions of nature by bringing together physicists working on scattering amplitudes and mathematicians with expertise in real, complex, tropical and computational algebraic geometry. The program features several mini-courses, two one-week topical workshops, as well as two weeks with a light program to enable collaborations among the participants.

Schedule (see below for details of topics):

Week 1, Feb 16-20: Mini-Courses I
Week 2, Feb 23-27: Light program (approx. one talk per day)
Week 3, Mar 2-6: Mini-Courses II
Week 4, Mar 9-13: Workshop I
Week 5, Mar 16-20: Light program (approx. one talk per day)
Week 6, Mar 23-27: Workshop II

Mini-Courses I. Expected lecturers include:

Melissa Sherman-Bennet: Amplituhedra
Bernd Sturmfels: Kinematic Varieties
Lorenzo Tancredi: Feynman Integrals

Mini-Courses II. Expected lecturers include:

Francis Brown: Introduction to Motivic and Mellin periods
Daniele Dorigoni: Modular Forms and AdS/CFT
James Drummond: Cluster Algebras
Samuel Grushevsky: Theta Functions and Moduli Spaces

Workshop I: Algebra and combinatorics of amplitudes, is co-organized by Thomas Lam, Erik Panzer, and Anastasia Volovich. Topics covered include: cluster algebras, amplituhedra and surfacehedra, tropical geometry, as well as positive and binary geometry.

Workshop II: Mathematical structures of amplitudes, is co-organized by Axel Kleinschmidt, Martin Raum, and Leila Schneps. It focusses on the mathematical properties of Feynman and string amplitudes. Topics covered include: Feynman/string integrals, their differential equations, (co-)homology theories and intersection numbers; computational aspects of periods, Hodge theory, theta functions, Siegel modular forms, and moduli spaces of curves and abelian varieties.

Funded by the European Union (ERC, MaScAmp, 101167287 and UNIVERSE PLUS, 101118787). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.