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Conference exploring the mathematical foundations of quantum field theory through the lens of positive geometries, cluster algebras, and the amplituhedron. Discover how these novel mathematical objects explain scattering amplitudes in particle physics and cosmology through a paradigm shift that connects algebraic combinatorics with quantum observables. Learn about the amplituhedron, introduced by Arkani-Hamed and Trnka in 2013, which provides geometric explanations for BCFW recurrence relations in N = 4 super Yang Mills theory, building upon Lusztig and Postnikov's work on positive Grassmannians. Explore the crucial role of cluster algebras, originally developed by Fomin and Zelevinsky for studying total positivity, in describing singularities of scattering amplitudes and their connections to positive geometries. Engage with introductory lectures covering cluster algebras, positive geometries, and scattering amplitudes, followed by expert presentations on topics including all-order splits, multi-soft limits, Grasstopes combinatorics, surface kinematics, affine cluster algebras, tropical amplituhedra, cosmological polytopes, and minimal kinematics. Participate in an open problems forum and hear from emerging scholars presenting cutting-edge research that bridges quantum field theory with advanced mathematical concepts. Access comprehensive coverage of how ideas from quantum field theory connect cluster algebras to positive geometries while discovering new examples of positive geometries through physical insights.
