Institut des Hautes Etudes Scientifiques (IHES) Courses

Inequalities Defining Polyhedral Realizations of Affine Types and Extended Young Diagrams

Explore crystal bases in Lie algebra representation theory, focusing on polyhedral realizations and explicit inequalities for classical affine types using extended Young diagrams.

• YouTube
• 44 minutes
• On-Demand
• Free Video

Combinatorics and Quantum Invariant Differential Operators on Reflection Equation Algebras

Explore quantum analogs of symmetric functions and differential operators in Reflection Equation Algebras, examining their properties and combinatorial applications.

• YouTube
• 43 minutes
• On-Demand
• Free Video

Elimination of Generators, Normal Forms, Indexed Computations and Iterated Smash-Products

Explore Lazard elimination theorems, their applications in algebra, and implementations in string rewriting and indexed computations for various mathematical structures.

• YouTube
• 42 minutes
• On-Demand
• Free Video

The Redei-Berge Symmetric Function of a Directed Graph

Explore symmetric functions in directed graphs, examining Redei's theorem on tournaments and Chow's path-cycle function. Discover new expansions and refinements in graph theory.

• YouTube
• 44 minutes
• On-Demand
• Free Video

Graph Complex Action on Poisson Structures: From Theory to Computation

Explore graph complex action on Poisson structures, from theoretical foundations to computational applications using SageMath's gcaops package for advanced mathematical research.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Introducing String Field Theory from a Geometrical Perspective

Explore string field theory's geometrical foundations, its construction from 2D CFT, and its connection to moduli spaces. Learn how neural networks aid in computing string theory potentials.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Macdonald Dualities in Genus One and Two

Explore Macdonald/Koornwinder polynomial dualities, from spherical Double Affine Hecke Algebra on a torus to genus two Macdonald theory, with Philippe Di Francesco.

• YouTube
• 45 minutes
• On-Demand
• Free Video

Analytic Stacks - New Foundations for Analytic Geometry

Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples.

• YouTube
• 1 hour 47 minutes
• On-Demand
• Free Video

Birational Invariants from Gromov-Witten Theory - Lecture 3

Explore birational invariants derived from Gromov-Witten theory, focusing on Iritani's theorem and its applications to proving non-rationality of geometric objects like cubic 4-folds.

• YouTube
• 2 hours 17 minutes
• On-Demand
• Free Video

Categorified Crystal Bases on Localized Quantum Coordinate Rings

Explore categorified crystal bases on localized quantum coordinate rings, focusing on monoidal categories, quiver Hecke algebras, and crystal structures in quantum algebra.

• YouTube
• 45 minutes
• On-Demand
• Free Video

New Initial Approximation in Loop Vertex Expansion for Quartic Matrix Models

Explore advanced techniques in Loop Vertex Expansion for QFT models, focusing on analytic continuation of free energy in quartic matrix models beyond standard cardioid domains.

• YouTube
• 39 minutes
• On-Demand
• Free Video

Tensor Models: From Matrix Models to Holography

Explore tensor models as a generalization of matrix models in quantum field theory, focusing on large N limit and double scaling mechanisms, with applications to holography.

• YouTube
• 43 minutes
• On-Demand
• Free Video

What Perturbative Field Theory Teaches Us About Statistical Analysis

Explore perturbative field theory's applications in particle physics, statistical mechanics, and functional analysis, focusing on divergence regularization and optimal transportation.

• YouTube
• 57 minutes
• On-Demand
• Free Video

Demi-Shuffle Duals of Magnus Polynomials in a Free Associative Algebra

Explore linear bases in free associative algebra: Magnus polynomials and their demi-shuffle duals. Discover applications to group-like series coefficients using Le-Murakami, Furusho type formulas.

• YouTube
• 38 minutes
• On-Demand
• Free Video

Analytic Stacks - Foundations for Analytic Geometry

Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with Peter Scholze.

• YouTube
• 1 hour 46 minutes
• On-Demand
• Free Video