Institut des Hautes Etudes Scientifiques (IHES) Courses

L'œuvre d'Alexandre Grothendieck - The Mathematical Legacy of Alexandre Grothendieck

Découvrez les idées révolutionnaires d'Alexandre Grothendieck en mathématiques à travers l'analyse experte de Pierre Deligne, explorant notamment le formalisme des six foncteurs et ses contributions fondamentales.

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

From Knot Invariants to Schur-Weyl Duality

Explore the connection between HOMFLY knot invariants and quantum group representation theory, examining their relationship to Hecke algebras and combinatorial mathematics.

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

New Identities for Differential-Polynomial Structures Built from Jacobian Determinants

Delve into advanced mathematical concepts exploring Nambu-determinant Poisson brackets, differential-polynomial identities, and their applications in classical mechanics and Lie algebras.

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

Decomposition Spaces in Combinatorics

Delve into the mathematical theory of decomposition spaces and their applications in combinatorics, exploring 2-Segal spaces and their computational properties through expert insights.

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

Partition Identities of the Andrews-Gordon Type - Commutative Algebra and Combinatorial Proofs

Delve into partition identities and the Andrews-Gordon theorems, exploring combinatorial proofs, Young diagrams, and q-series identities in advanced mathematical research.

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

Algebraicity Beyond Beukers-Heckman and Bober - Emerging Patterns in Factorial Ratios

Delve into advanced mathematical concepts exploring algebraic generating functions, factorial ratios, and hypergeometric functions through innovative approaches to sequence analysis and moment problems.

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

Eilenberg-Schützenberger Machines, States, Sigma-Modules and Applications

Delve into multiplicity automata behavior, exploring matrix operations, Sweedler's duals, and topological algebras, culminating in a novel two-state transducer for the Collatz function.

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

Computational Complexity in Column Sums of Symmetric Group Characters

Delve into computational complexity theory through symmetric group character analysis, exploring column sums, combinatorial topology, and branched covers of spheres in theoretical physics.

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

Matrices Filled by Variables: From Posets to Coxeter Groups and Beyond

Explore advanced matrix theory through variable-filled matrices, examining their eigenvalue properties across posets, reflection groups, and beyond in theoretical mathematics.

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

Crystal Structure of Localized Quantum Unipotent Coordinate Category

Delve into advanced mathematical concepts exploring crystal structures, quantum unipotent coordinate categories, and their relationships with Kac-Moody Lie algebras through rigorous theoretical frameworks.

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

On the Injective Norm of Random Tensors and Quantum States

Delve into advanced quantum information theory through an exploration of injective norms in random tensors, geometric entanglement, and multispecies spherical spin glass models with mathematical precision.

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

Higher Bruhat Orders and Higher Operads

Delve into advanced mathematical concepts exploring higher d-operads and their relationship with higher Bruhat orders on discrete Grassmannians, featuring insights from collaborative research.

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

Functional Equations for Motivic Generating Series of Kronecker Moduli

Delve into advanced mathematical concepts exploring Kronecker moduli, their generating series, and functional equations, with focus on algebraicity and q-difference equations in linear algebra.

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

Reflection Equation Algebras vs Quantum Groups in Combinatorics and Mathematical Physics

Explore the comparative analysis of Reflection Equation Algebras and Quantum Groups, focusing on their applications in Combinatorics and Mathematical Physics, including the Quantum Capelli identity.

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

Monomial Identities in the Weyl Algebra - A Combinatorial and Computational Approach

Delve into advanced algebraic concepts exploring monomial identities in Weyl algebra, covering operational characterizations, lattice path invariants, and rook theory applications in characteristic 0 fields.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video