Institut des Hautes Etudes Scientifiques (IHES) Courses

Positive Scalar Curvature with Point Singularities

Explore topological construction of positive scalar curvature metrics with Euclidean point singularities, challenging Schoen's conjecture and geometric flow limitations.

• YouTube
• 1 hour 21 minutes
• On-Demand
• Free Video

How Hard is the Theorem of Stolz - Metrics and Scalar Curvature in Spin Manifolds

Delve into the complexity of Stolz's theorem on positive scalar curvature metrics, exploring metric deformations and manifold transformations through groundbreaking mathematical research findings.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Localization Theory for Harish-Chandra Bimodules in Positive Characteristic

Delve into advanced algebraic group theory, exploring Harish-Chandra bimodules, equivariant coherent sheaves, and their connections to representation theory in positive characteristic mathematics.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

On the Left Adjoint of mod p Smooth Parabolic Induction

Delve into advanced mathematical concepts exploring parabolic induction functors, focusing on left adjoint properties and their behavior with algebraic weights in p-adic field extensions.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Relative Poincaré Duality in Non Archimedean Geometry

Delve into advanced mathematical concepts exploring relative mod-p Poincaré duality in rigid-analytic varieties, featuring novel trace map constructions and diagrammatic proofs for smooth morphisms.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

q-Higgs Modules and the Nygaard Filtration in Prismatic Cohomology

Delve into advanced mathematical concepts of prismatic crystals, q-Higgs modules, and their cohomology, exploring Frobenius isogeny properties and Nygaard filtration in prismatic F-crystal theory.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Holomorphic-Topological Twists and Their Applications

Explore holomorphic-topological twists in supersymmetric quantum field theories, examining mathematical properties, formality results, categorical wall-crossing, and 't Hooft expansion approaches.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

An Update on SYZ Mirror Symmetry and Family Floer Theory

Explore Strominger-Yau-Zaslow approach to homological mirror symmetry, focusing on Lagrangian torus fibrations and Fukaya-Floer algebra construction for mirror symmetry in complex geometry.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Universally Counting Curves in Calabi-Yau Threefolds

Explore a universal enumerative invariant for curves in algebraic varieties, focusing on threefolds with nef anticanonical bundle and its implications for the MNOP conjecture.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

A-Infinity Functor in Symplectic Geometry and Gauge Theory

Explore advanced concepts in Floer theory, focusing on representability of A-infinity functors in symplectic geometry and gauge theory applications.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Combinatorics and Geometry of the Amplituhedron

Explore the amplituhedron's geometric properties, connections to various mathematical fields, and recent progress on key conjectures in this advanced mathematical lecture.

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

Geometric Quantization of General Kahler Manifolds

Explore geometric quantization on Kähler phase spaces, examining function quantization, Hilbert space structure, and Kähler structure dependence. Investigate curvature's impact on quantization.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Birational and Singularity Invariants from Non-Commutative Hodge Theory

Explore new additive invariants of smooth projective varieties called Hodge atoms, their applications to birational equivalence, and novel singularity invariants in algebraic geometry.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Motivic Invariants of Moduli of Irregular Parabolic Higgs Bundles and Bundles

Explore motivic integration and its application to Donaldson-Thomas invariants in moduli stacks of semistable irregular parabolic Higgs bundles and connections on projective curves.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Some Applications of Non-Abelian Hodge Theory

Explore applications of non-abelian Hodge theory in studying meromorphic flat bundles and holonomic D-modules, including Barannikov-Kontsevich theorem and irregular Hodge filtration.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video