Algebraic Geometry Courses and Certifications

BunG Seminar

Cuspidal Hecke Eigensheaves via Localization - Talk 19

Delve into advanced mathematical concepts exploring Beilinson-Drinfeld's construction of cuspidal Hecke eigensheaves and their relationship with Kac-Moody representations.

• YouTube
• 2 hours 7 minutes
• Self-Paced
• Free Video

BunG Seminar

Miraculous Duality and Applications to Eisenstein Series - Talk 18

Delve into advanced mathematical concepts of D-modules, self-duality, and Eisenstein series through an exploration of Bun_G stack properties and miraculous duality theorems.

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

BunG Seminar

Algebraic D-Modules: A Basic Review - Talk 12

Dive into the fundamentals of algebraic D-modules through a comprehensive review based on J. Bernstein's notes, exploring key concepts and theoretical foundations.

• YouTube
• 1 hour 36 minutes
• Self-Paced
• Free Video

BunG Seminar

Compact Generation of D-modules on BunG - Talk 15

Delve into advanced mathematical concepts of D-modules on Bun_G, exploring compact generation, DG categories, and applications in algebraic geometry through detailed theoretical analysis.

• YouTube
• 1 hour 36 minutes
• Self-Paced
• Free Video

BunG Seminar

Uniformization of Principal Bundles - Talk 8

Delve into advanced algebraic geometry concepts exploring uniformization maps, affine Grassmannians, and principal G-bundles over complex projective curves with expert Minh-Tâm Trinh.

• YouTube
• 1 hour 35 minutes
• Self-Paced
• Free Video

BunG Seminar

Geometric Contractiveness of the Harder-Narasimhan Stratification in BunG - Talk 10

Delve into the geometric contractiveness of Harder-Narasimhan stratification and its implications for D-modules on BunG, exploring behavior at infinity and quasi-compact properties.

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

BunG Seminar

Infinitesimal Structure of BunG and Jet Spaces - Talk 11

Delve into advanced mathematical concepts exploring jet spaces, principal G-bundles, and conformal blocks for Kac-Moody algebras through an in-depth analysis of BunG's infinitesimal structure.

• YouTube
• 1 hour 41 minutes
• Self-Paced
• Free Video

BunG Seminar

The Harder-Narasimhan Filtration and Stability Conditions for Vector Bundles

Delve into the mathematical theory of stability conditions and Harder-Narasimhan filtration for vector bundles, exploring their applications in geometric invariant theory and moduli spaces.

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

BunG Seminar

Algebraicity of BG and BunG - Talk 3

Delve into algebraic stacks theory, exploring classifying stack BG and Bun_{G,X}, with focus on GL_n groups and smooth projective curves, including Weil's automorphic interpretation.

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

BunG Seminar

Functor of Points and Descent - Talk 2

Delve into advanced algebraic geometry concepts, exploring schemes, stacks, and topology through the lens of functor points and descent theory in this mathematical seminar.

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

BunG Seminar

Examples and Basic Properties of BunG - Talk 9

Explore concrete examples of BunG geometry through explicit polynomial computations, focusing on P^1 cases and examining vector bundles, G-torsors, and Ramanathan's deformation theory.

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

Kyoto-U OCW - Unofficial

Curve Counting, Geometric Representation Theory, and Quantum Integrable Systems - Lecture 2

Delve into advanced mathematical concepts exploring curve counting, geometric representation theory, and quantum integrable systems with Professor Andrei Okounkov's expert analysis and insights.

• YouTube
• 2 hours 4 minutes
• Self-Paced
• Free Video

University of Chicago Department of Mathematics

Proof of the Geometric Langlands Conjecture

Delve into advanced mathematical concepts exploring the Geometric Langlands Conjecture, including de Rham, Betti, and l-adic contexts, presented by Dennis Gaitsgory with collaborative insights.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Stony Brook Mathematics

Stable Degenerations of Singularities

Explore stable degenerations of singularities in algebraic geometry, focusing on Li-Xu's Stable Degeneration Conjecture and its implications for metric tangent cones in Kähler-Einstein manifolds.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Stony Brook Mathematics

Real Loci of Non-Real Varieties - Mathematics Department Colloquium

Explore cooriented submanifolds in real algebraic geometry, focusing on their properties, intersections, and linking numbers. Gain insights into the geometry of pencils and real projective spaces.

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