Explore advanced mathematical concepts at the intersection of discrete mathematics, number theory, and theoretical physics through this comprehensive conference featuring 26 specialized lectures. Delve into computability-focused problems drawn from renormalization theory, combinatorial physics, geometry, and evolution equations, with emphasis on both commutative and noncommutative frameworks. Examine computational approaches utilizing combinatorial structures including graphs, trees, words, automata, and semirings, alongside classical mathematical structures such as operators, Hopf algebras, and special functions. Investigate cutting-edge research in Fock spaces associated with Coxeter groups, topological data analysis in visual art perception, hypergeometric counting of restricted set partitions, and Manin-Schechtman orders for directed graphs. Study tropical algebraic geometry through the Nullstellensatz and Positivstellensatz, partition counting by genus, and effective homology for hypersurface periods. Discover quantum entanglement solutions to classical problems, integer eigenvalue phenomena, and Magnus polynomials in free associative algebras. Learn about limit shapes from skew Howe duality, tensor models, perturbative field theory applications to statistical mechanics, and loop vertex expansion techniques. Explore categorified crystal bases on quantum coordinate rings, Macdonald dualities in higher genus, and quantum relativistic Toda Hamiltonians connected to cluster algebras. Examine symmetric functions of directed graphs, elimination of generators in normal forms, quantum invariant differential operators on reflection groups, and polyhedral realizations of affine types. Investigate string field theory from geometrical perspectives, graph complex actions on Poisson structures, computer algebra solutions to combinatorial equations, twisted quantum double models, and combinatorial topological quantum field theories with their geometrical interpretations.

Syllabus

Marek Bożejko - Fock spaces associated with Coxeter groups of type B
Marek Kuś - Perception of visual art and topological data analysis
Karol Penson - Counting restricted set partitions with hypergeometrics
Gleb Koshevoy - On Manin–Schechtman orders related to directed graphs
Stéphane Gaubert - The Nullstellensatz and Positivstellensatz for Sparse Tropical (...)
Jean-Bernard Zuber - Counting partitions by genus
Eric Pichon-Pharabod - Periods of hypersurfaces via effective homology
Karol Zyczkowski - Thirty-six entangled officers of Euler:quantum solution of a classically (...)
Maxim Kontsevich - The miracle of integer eigenvalues
Hiroaki Nakamura - Demi-shuffle duals of Magnus polynomials in a free associative algebra
Travis Scrimshaw - Limit shapes from skew Howe duality
Adrian Tanasa - Tensor models
Andrea Sportiello - What does perturbative field theory teaches us on the statistical (...)
Vasily Sazonov - New Initial Approximation in Loop Vertex Expansion
Toshiki Nakashima - Categorified Crystal Bases on Localized Quantum Coordinate Rings and (...)
Philippe Di Francesco - Macdonald dualities in genus one and two
Rinat Kedem - Quantum relativistic Toda Hamiltonians associated with a family of cluster algebras
Darij Grinberg - The Redei–Berge symmetric function of a directed graph
Gérard Duchamp - Elimination of generators, normal forms, indexed computations and iterated (...)
Dimitry Gurevich - Combinatorics and quantum invariant differential operators on Reflection (...)
Yuki Kanabuko - Inequalities defining polyhedral realizations of affine types and extended (...)
Harold Erbin - Introducing string field theory from a geometrical perspective
Ricardo Buring - Graph complex action on Poisson structures: from theory to computation
Hadrien Notarantonio - Solving equations from combinatorics via computer algebra
Thomas Krajewski - A twisted version of Kitaev’s quantum double model
Sanjaye Ramgoolam - Combinatorial topological quantum field theories and geometrical (...)