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Explore a comprehensive workshop that examines the powerful synergies between combinatorial methods and their applications in algebraic geometry and number theory. Delve into two extensive mini-courses: Kris Shaw's exploration of Combinatorial Geometry and Hodge Theory, and Farbod Shokrieh's investigation of Berkovich Spaces, Tropical Geometry and Number Theory. Discover cutting-edge research through expert presentations covering diverse topics including inequalities for trees and matroids, tropical semirings and curve singularities, Chern-Weil theory for singular metrics, vector-valued polynomial equations and toric vector bundles, Lorentzian polynomials and matroids over triangular hyperfields, positive del Pezzo geometry, toric equidistribution, and compactified Jacobians. Gain insights from emerging researchers presenting their work on hybrid spaces in Deligne-Mumford stacks, alternative modular compactifications, p-adic integration theories, polyhedral tiltings, tropical Abel-Prym maps, singular matroid realization spaces, uniform rank refinements, and string polytopes in Arakelov geometry. Learn from an international faculty of mathematicians and young researchers representing institutions across the Americas, Europe, and Asia, all focused on advancing combinatorial methods in the study of geometric and arithmetic structures.
