Explore the intersection of combinatorics and fundamental physics through this comprehensive workshop featuring 20 specialized lectures from leading researchers at the Institute for Advanced Study. Delve into cutting-edge topics including polypositroids, correlators and amplitudes, wondertopes, and Yang-Mills theory loop integrands. Examine the mathematical foundations underlying particle physics through discussions of rational normal curves, ABCT varieties, and canonical bases for cosmological correlators. Investigate advanced algebraic structures including Hopf algebras in cohomology, topological aspects in algebraic optimizations, and combinatorics on words in string amplitudes. Learn about loop integration techniques, phenomenological applications, and prospects for computational improvements in theoretical physics calculations. Discover the geometric properties of amplituhedra, configuration space theory, and canonical differential forms. Study cluster structures on kinematic spaces, oriented matroid canonical forms, and Euler discriminants of hyperplane complements. Analyze kinematic flow and differential equations for cosmological correlators, symbol alphabets in N=4 Yang-Mills theory, and moduli space cohomology probed through quantum field theory. Conclude with explorations of amplituhedra and origami connections, providing a comprehensive overview of how combinatorial methods illuminate fundamental physics phenomena.

Syllabus

Polypositroids - Alex Postnikov
Aspects of Correlators and Amplitudes - Song He
Wondertopes - Raluca Vlad
Loop integrands in Yang-Mills theory from the forward limit - Qu Cao
Points on rational normal curves and the ABCT variety - Dawei Shen
A canonical basis for cosmological correlators from the positive geometry of cuts - Shounak De
Hopf Algebras in the Cohomology of A_g - Melody Chan
Topological Aspects in Algebraic Optimizations - Botong Wang
Combinatorics on Words in String Amplitudes - Oliver Schlotterer
Loop Integration: Phenomenology, Polemics, and Prospects for Improvement - Jacob Bourjaily
Combinatorics and Geometry of the Amplituhedron - Lauren Williams
Adventures in Configuration Space - Nick Early
Adjoints and Canonical Differential Forms - Simon Telen
Cluster Structures on Kinematic Spaces - Lara Bossinger
Canonical Forms of Oriented Matroids - Chris Eur
Euler Discriminant of Complements of Hyperplanes - Claudia Fevola
Kinematic Flow and Differential Equations for Cosmological Correlators - Austin Joyce
Combinatorics of Symbol Alphabets in N=4 Yang-Mills - Anastasia Volovich
Probing Moduli Space Cohomology Using Quantum Field Theory - Michael Borinsky
Amplituhedra and Origami - Pavel Galashin