Institut des Hautes Etudes Scientifiques (IHES) Courses

Renormalization Group Methods for Quantum Spin Glasses

Explore renormalization group methods for quantum p-spin glass dynamics using Wetterich-Morris formalism, examining symmetric and broken phases with nonperturbative approaches.

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

Macdonald Functions and Quantum Dilogarithm

Explore advanced connections between Macdonald functions and quantum dilogarithms in type A, featuring new Givental-like expressions and cluster algebra realizations.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

Łukasiewicz Logic and Tsallis Entropy Connected with Free Projections in Probability Theory

Explore advanced connections between Łukasiewicz logic, Tsallis entropy, and free projections in noncommutative probability theory through rigorous mathematical analysis.

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

Persistence Probabilities for Random Walks and Related Processes

Explore persistence probabilities in random walks, autoregressive sequences, and moving averages through generating functions and their connections to special mathematical functions.

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

Phase Transitions and Mittag-Leffler Functions for Critical Schemes Under q-Enumeration

Explore phase transitions in combinatorial structures through q-enumeration, revealing Mittag-Leffler distributions at critical points and Gaussian behavior in supercritical regimes.

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

Minimal Polynomial Parameterization of Rational Knots

Explore polynomial parameterizations of knots in 3-space, focusing on determining minimal lexicographic degrees for two-bridge knots using algebraic geometry and braid theory methods.

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

Combinatorics and Arithmetic of Lissajous 3-Braids

Explore the classification of braids from 3-body Lissajous curve motions, examining continued fractions, cutting sequences, and symbolic frieze patterns in this advanced mathematics research.

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

Källén Function and Around

Explore the remarkable Källén function, from its mathematical origins to applications in physics, combinatorics, and differential equations with connections to hypergeometric functions.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Higher Dimensional Floorplans and Baxter d-Permutations

Explore higher-dimensional generalizations of mosaic floorplans and their bijections with Baxter d-permutations, including generating trees and forbidden vincular patterns.

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

Quantum Error Mitigation Driven by Classical Simulations and Evolution Equations

Explore quantum error mitigation techniques using classical simulations and evolution equations to overcome noise in quantum hardware for complex physical systems.

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

Steinberg Symbol and Tau Function

Explore Steinberg symbols as multiplicative bicharacters and their connection to tau functions, Heisenberg groups, and boson-fermion correspondence in advanced mathematical physics.

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

Invitation to Random Tensor Models - From Random Geometry to Enumeration and Characteristic Polynomials

Explore random tensor models from quantum gravity motivation to graph enumeration and characteristic polynomials via Grassmann integrals with recent research findings.

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

On Recent Conjectures Concerning Free Jordan Algebras and Free Alternative Algebras

Explore recent conjectures on free Jordan and alternative algebras, examining why proposed theories fail and uncovering new computational insights into these mysterious structures.

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

Remarks on Certain Parametrized Algebraic Equations

Explore parametrized algebraic equations linking integer sequences through exponential generating functions, featuring hypergeometric solutions and moment problems.

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

Characterization of the Unit Object in Localized Quantum Unipotent Category

Explore advanced algebraic structures through quiver Hecke algebras and localized quantum unipotent categories, focusing on crystal structures and unit object characterization.

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