Explore advanced mathematical concepts at the intersection of discrete mathematics, number theory, and theoretical physics through this comprehensive conference featuring 20 specialized lectures from leading researchers. Delve into cutting-edge topics including algebraic hypergeometric series, executable applied category theory, maximally dense sphere packings, and noncommutative birational operations on mathematical structures. Examine computational approaches based on combinatorial structures such as graphs, trees, words, and automata, alongside classical structures including operators, Hopf algebras, and special functions. Investigate applications to theoretical physics problems including renormalization, combinatorial physics, geometry, evolution equations, and noncommutative differential equations. Learn about crystal operators on cluster algebras, string cones and cluster varieties, tropical versions of Hilbert polynomials, and ambitropical convexity in mean payoff games. Discover enumerative combinatorics through trimer covers, Young tableaux with walls, and the density method for generation algorithms. Study advanced topics in algebraic geometry and linear logic, anomalous statistics of extreme random processes, and solutions to Knizhnik-Zamolodchikov differential equations. Gain insights into the geometric foundations of matter and physics, asymptotic distributions in trivalent maps, and Yang-Zagier generating functions through presentations by internationally recognized experts including Maxim Kontsevich and other distinguished mathematicians and physicists.

Syllabus

Maxim Kontsevich - An Update on Algebraic Hypergeometric Series
Nicolas Behr - Towards Executable Applied Category Theory in Coq
Thomas Fernique - Maximally Dense Sphere Packings
Dimitry Gurevich - q-cut-and-join Operators and q-Capelli Identity on Reflection Equation Algebras
Darij Grinberg - Noncommutative Birational Rowmotion on Rectangles
Volker Genz - Crystal Operators on Cluster Algebras
Bea Schumann - String Cones and Cluster Varieties
James Propp - Conjectural Enumerations of Trimer Covers of Finite Subgraphs of the Triangular (...)
Vincent Rivasseau, Léonard Ferdinand - Some New Taylor-BKAR Formulas
Paul-André Melliès - A Functorial Excursion between Algebraic Geometry and Linear Logic
Richard Kerner - Geometry, Matter and Physics
Alexandros Singh - Asymptotic Distribution of Parameters in Trivalent Maps and Linear Lambda Terms
Sergey Yurkevich - How to Conjecture and Prove that the Generating Function of the Yang-Zagier (...)
Sergei Nechaev - Anomalous Statistics of Extreme Random Processes
Frédéric Patras - Noncommutative Wick Polynomials
Cyril Banderier - Enumeration and Generation of Young Tableaux with Walls: the Density Method
Dimitri Grigoryev - A Tropical Version of Hilbert Polynomial
Stéphane Gaubert - Ambitropical Convexity, Mean Payoff Games and Nonarchimedean Convex Programming
Vincel Hoang Ngoc Minh - On the Solutions of Knizhnik-Zamolodchikov Differential Equations by (...)
Lionel Pournin - Distance, Strong Convexity, Flagness, and Associahedra