Algebraic Geometry Courses and Certifications

Institut des Hautes Etudes Scientifiques (IHES)

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

Institut des Hautes Etudes Scientifiques (IHES)

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

Institut des Hautes Etudes Scientifiques (IHES)

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

Institut des Hautes Etudes Scientifiques (IHES)

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

Institut des Hautes Etudes Scientifiques (IHES)

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

Institut des Hautes Etudes Scientifiques (IHES)

Solving Equations from Combinatorics via Computer Algebra

Explore advanced techniques for solving discrete differential equations in combinatorics using computer algebra, focusing on efficient methods for n=2 cases and recent developments in systems of equations.

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

Institut des Hautes Etudes Scientifiques (IHES)

Periods of Hypersurfaces via Effective Homology

Explore numerical approximations of periods for hypersurfaces using effective homology, enabling computation of algebraic invariants for complex projective varieties.

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

Institut des Hautes Etudes Scientifiques (IHES)

Kummer Extensions: Applications to Generalized Cross-Ratios and Functions on Hilbert Schemes

Explore Kummer extensions in geometry and arithmetic, including generalized cross-ratios and functions on Hilbert schemes. Gain insights into advanced algebraic geometry concepts.

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

Institut des Hautes Etudes Scientifiques (IHES)

Prismatic Cohomology Relative Delta-Rings

Explore prismatic cohomology's evolution, comparing absolute and relative variants, and delve into a new generalization bridging the two approaches.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Motivic Cohomology of Schemes - Lecture 3

Explore advanced motivic cohomology theory for equicharacteristic schemes, covering cdh topology, K-theory filtration, and applications to algebraic geometry and zero cycles.

• YouTube
• 1 hour 28 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Introduction to Prismatic Cohomology - Lecture 4

Explore prismatic cohomology, focusing on prismatization and the prismatic logarithm in advanced algebraic geometry and number theory.

• YouTube
• 1 hour 37 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Introduction to Prismatic Cohomology - Lecture 3

Explore prismatic cohomology, covering general results, prismatization, and the prismatic logarithm in this advanced mathematics lecture by Johannes Anschütz.

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

Institut des Hautes Etudes Scientifiques (IHES)

Introduction to Prismatic Cohomology - Lecture 2

Explore prismatic cohomology, focusing on general results and derived concepts. Delve into prismatization as a tool for understanding this advanced mathematical theory.

• YouTube
• 1 hour 32 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

A Homotopical Approach to Crystalline Cohomology

Explore a homotopical approach to crystalline cohomology, focusing on higher homotopies for canonical lifts and easier global definition through gluing.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Cambridge University Press

Weight Zero Compactly Supported Cohomology of Hg,n - Forum of Mathematics Video Series

Explore the moduli space Hg,n and its algebraic structure in this mathematical video presentation on weight zero compactly supported cohomology research.

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