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Explore the intersection of combinatorial methods with algebraic geometry through this comprehensive conference featuring lectures on tropical geometry and real algebraic geometry. Delve into cutting-edge research through four main lecture series covering geometry of tropical varieties with applications, optimization and tropical combinatorics, algebraic and convex geometry of sums of squares on varieties, and vector bundles on Riemann surfaces and metric graphs. Examine specialized topics including circular fence posets and associated polytopes, forbidden patterns in tropical planar curves, shrinking dynamics on tropical series, scattering amplitudes from positive geometries, Newton polytopes in reaction networks, and tropical intersection theory with polytope algebra. Investigate advanced concepts such as quantum geometry of matroids, tropical limits of string theory and Feynman integrals, tropical quantum field theory with mirror polyvector fields, dimers and Beauville integrable systems, and the continuous associahedron of type A. Learn about connections between gentle algebras and S-matrix in quantum field theory, bitangents to plane quartics across tropical, real and arithmetic contexts, updates on tropical schemes, and large deviations for random hives. Gain insights into singular Hodge theory for combinatorial geometries, generalizations of GKZ secondary fans using Berkovich geometry, vertex gluings and Demazure products, and parameter estimation in reaction networks through this intensive mathematical conference organized by the International Centre for Theoretical Sciences.
