Institut des Hautes Etudes Scientifiques (IHES) Courses

Local Systems and Higgs Bundles in p-adic Geometry

Explore the algebraic nature of local systems and Higgs bundles in p-adic geometry, drawing parallels to complex varieties and characteristic p counterparts.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Analytic Prismatization - Extending Prismatic Cohomology to Rigid-Analytic Spaces

Explore prismatic cohomology's extension to rigid-analytic spaces, including degeneration from analytic Hodge-Tate stack to Ogus-Vologodsky correspondence in characteristic p.

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

Characteristic Classes of Étale Local Systems

Explore characteristic classes of étale Z_p-local systems on algebraic varieties, their relation to Chern-Simons classes, and connections to Hodge filtration in p-adic settings.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Motives and Super-Representation Theory: Principles and Case Studies

Découvrez les principes et études de cas des motifs et de la (super-)théorie des représentations, explorant la théorie de Galois motivique abstraite.

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

The Non-Abelian p-Curvature Conjecture

Explore a generalized p-curvature conjecture for non-linear ODEs, its implications for algebraic geometry, and proof techniques inspired by Katz and Esnault-Groechenig's work.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Characteristic Cycle and Pushforward for L-adic Sheaves

Explore characteristic cycles for l-adic sheaves, their role in measuring ramification, and the compatibility of pushforward along proper morphism in this advanced mathematical lecture.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Vanishing Theorems for the Irregular Hodge Filtration

Explore recent advances in irregular Hodge filtration, focusing on Kodaira vanishing theorems similar to Saito's for mixed Hodge modules.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Positive Mass Theorem for Asymptotically Flat Manifolds with Isolated Conical Singularities

Explore recent advancements in positive mass theorem for asymptotically flat manifolds with isolated conical singularities, covering spin and non-spin settings, analysis techniques, and Geroch-type results.

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

Positive Mass Theorem and Positive Scalar Curvature with Singularities

Explore recent developments in positive mass theorem and scalar curvature, focusing on singular metrics and isolated conical singularities in mathematical physics.

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

Finiteness Questions for Étale Coverings with Bounded Wild Ramification

Explorez les coverings étales des variétés en caractéristique positive, leurs ramifications et les problèmes ouverts associés dans cette présentation mathématique avancée.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Donaldson-Thomas Invariants: Classical, Motivic, Quadratic and Real

Explore advanced Donaldson-Thomas invariants in algebraic geometry, including classical, motivic, quadratic, and real variants. Delve into virtual fundamental classes and refined invariants.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

The Bloch-Esnault-Kerz Fiber Square in p-adic Hodge Theory

Explore the Bloch-Esnault-Kerz theorem, Beilinson's generalization, and Clausen's proposal for defining the Hodge-Tate period map in p-adic Hodge theory and algebraic K-theory.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

Secondary Invariants and Arithmetic Rigidity

Explore secondary Chern classes in complex local systems, their definitions, and arithmetic analogs. Delve into rigidity phenomena and motivic speculations in algebraic geometry.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Various Remarks on the Donagi-Pantev Program for Construction of Hecke Eigensheaves

Explore the Donagi-Pantev program for constructing Hecke eigensheaves, examining known cases, challenges, and connections to Hitchin moduli space geometry.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Different Notions of Tameness Revisited in Étale Morphisms

Explore different approaches to defining tameness in étale morphisms of schemes, focusing on valuation-theoretic methods and nonarchimedean geometry to overcome limitations of compactification-based approaches.

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