Institut des Hautes Etudes Scientifiques (IHES) Courses

Reddening Sequences for Cluster Algebras

Explore reddening sequences in cluster algebras, their implications, and known cases, delving into finite dimensionality, invariants, and canonical bases.

• YouTube
• 44 minutes
• Self-Paced
• Free Video

Introduction to Resurgence in Asymptotic Expansions - Lecture

Explore resurgence in Stirling formula and quantum dilogarithm, examining asymptotic expansions and the interplay between large and small coefficients in mathematical series.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Hausdorff Moment Problems for Combinatorial Numbers: Heuristics via Meijer Functions

Explore Hausdorff moment problems for combinatorial sequences, focusing on integral ratios of factorials. Learn techniques to solve these problems and discover patterns in Meijer G-function encodings.

• YouTube
• 45 minutes
• Self-Paced
• Free Video

Substitutions in Non-Commutative Multivariate Power Series

Explore group laws on non-commutative formal power series, their structures, and applications in non-commutative probability theory through a Hopf algebraic approach.

• YouTube
• 46 minutes
• Self-Paced
• Free Video

Creative Telescoping for the Canham Model in Genus 1

Explore Creative Telescoping's application in biological physics, focusing on biomembrane shapes and the Helfrich problem for genus 1 surfaces using Clifford torus projections and hypergeometric functions.

• YouTube
• 40 minutes
• Self-Paced
• Free Video

Random Lattices as Sphere Packings

Explore lattice-sum functions and their applications in sphere packing density, including Siegel's mean value theorem and recent advancements in optimal packing bounds.

• YouTube
• 33 minutes
• Self-Paced
• Free Video

Strange Gradings and Elimination of Generators

Explorez les liens entre l'élimination des générateurs et diverses théories combinatoires, avec des applications aux décompositions semi-directes.

• YouTube
• 46 minutes
• Self-Paced
• Free Video

A Gentle Introduction to Template Games and Linear Logic

Explore game semantics, template games, and linear logic through interactive interpretations of formulas and proofs, focusing on scheduling policies and compositional strategies.

• YouTube
• 45 minutes
• Self-Paced
• Free Video

Categorification of Rule Algebras in Compositional Rewriting Systems

Explore a novel approach to formalizing operations in compositional rewriting systems, focusing on double categories and presheaf calculus for counting rewrite realizations.

• YouTube
• 41 minutes
• Self-Paced
• Free Video

Théorie des Cordes et Théorie des Nombres : Valeurs Multiples Zêta et Amplitudes Physiques

Explorez les liens fascinants entre la théorie des nombres et les amplitudes physiques, en mettant l'accent sur l'univaluation et l'invariance modulaire.

• YouTube
• 2 hours 10 minutes
• Self-Paced
• Free Video

Amplitudes de Cordes et Équations de Type Knizhnik-Zamolodchikov

Explorez les avancées récentes dans la compréhension des amplitudes de cordes et leurs liens avec les équations de Knizhnik-Zamolodchikov, en mettant l'accent sur les relations entre cordes ouvertes et fermées.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Harnessing SL(2, Z) in Super Yang-Mills and Gravity

Explore new approaches to S-duality in N=4 super Yang-Mills theory using SL(2,Z) harmonic analysis, revealing constraints on observables and implications for holography.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Random Field Ising Model and Parisi-Sourlas Supersymmetry - Lecture 4

Explore the Random Field Ising Model, Parisi-Sourlas supersymmetry, and dimensional reduction. Delve into recent theories explaining numerical evidence and potential loss of supersymmetry in specific dimensions.

• YouTube
• 1 hour 48 minutes
• Self-Paced
• Free Video

Scalar Curvature Rigidity in Manifolds

Explore scalar curvature rigidity in manifolds, examining known solutions and current research questions using spinorial techniques.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

Scalar Curvature Rigidity and Extremality in Dimension 4

Explore scalar curvature rigidity in 4D using Finsler-Thorpe trick and twisted spinor methods. Discover area-extremal properties of 4-manifolds with nonnegative sectional curvature.

• YouTube
• 46 minutes
• Self-Paced
• Free Video