Combinatorics and Arithmetic for Physics

Explore advanced mathematical concepts at the intersection of discrete mathematics, number theory, and theoretical physics through this comprehensive conference featuring leading researchers from Institut des Hautes Etudes Scientifiques. Delve into cutting-edge topics including combinatorial structures, Hopf algebras, renormalization theory, and noncommutative differential equations with emphasis on computational approaches and computer-based implementation. Examine tracelet algebras, dialogue games in string diagrams, untyped linear lambda calculus, constructive matrix theory, and quantum mechanics of bipartite ribbon graphs through expert presentations. Investigate tropical convexity, mean payoff games, reflection equation algebras, and Kleene stars in shuffle algebras while discovering connections between symmetric polynomial rings and Grassmannian cohomology. Learn about MRS factorizations, noncommutative Poisson structures, Hopf-algebraic renormalization of multiple zeta values, and Z3-graded Lorentz-Poincaré algebra unification with colour SU(3). Gain insights into maximal green sequences for triangle products, tropical versions of the Jacobian conjecture, and highly noncommutative words through presentations by renowned mathematicians and physicists including Nicolas Behr, Paul André Melliès, Noam Zeilberger, Vincent Rivasseau, and others, organized by Gérard H.E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, and Hoang Ngoc Minh.