Combinatorics and Arithmetic for Physics - Special Days 2022

Explore advanced mathematical concepts at the intersection of discrete mathematics, number theory, and theoretical physics through this comprehensive conference series. Delve into computability questions with emphasis on renormalization, combinatorial physics, geometry, and evolution equations drawn from theoretical physics models. Examine computational approaches based on combinatorial structures including graphs, trees, words, automata, and semirings, as well as classical structures such as operators, Hopf algebras, evolution equations, special functions, and categories suitable for computer-based implementation and experimentation. Learn from leading experts presenting on diverse topics including categorification of rule algebras, template games and linear logic, random lattices as sphere packings, geometry and physics of covalent network glasses, phase transitions of composition schemes, creative telescoping methods, Hausdorff moment problems for combinatorial numbers, substitutions in non-commutative multivariate power series, reflection equation algebras, resurgence theory, cycle shuffles in symmetric group algebra, canonical Grothendieck polynomials, statistical models on random regular graphs, cluster algebras and reddening sequences, positivity of Meijer G-functions, Landau-Ginzburg potentials, cluster duality and spectral curves, and combinatorics of the amplituhedron. Gain insights into cutting-edge research methodologies that bridge pure mathematics with computational physics applications through presentations by renowned mathematicians and physicists from the Institut des Hautes Etudes Scientifiques.