Chern Class Courses and Certifications

Institut des Hautes Etudes Scientifiques (IHES)

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
• On-Demand
• Free Video

ICTP Mathematics

Hyperkähler and Prym Varieties - Classical and New Results

Explore advanced algebraic geometry through hyperkähler manifolds and Prym varieties, covering classical theory, recent advances, and open problems in this specialized mathematical field.

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

ICTP Mathematics

ICTP-IGAP Seminar on Algebraic Geometry - Representations of the Diagonal for Moduli Spaces of Sheaves

Explore representations of the diagonal for moduli spaces of sheaves, focusing on cohomology, Chow rings, and Lie algebra actions. Gain insights into algebraic geometry and holomorphic symplectic geometry.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

IMSA

Extensions in MHM and Hain's Biextension Line Bundle - Part 2

Explores biextension line bundles, their extensions, and algebraic structures. Presents a formula for Q-line bundles, building on Hain and Pearlstein's work on normal functions and complex manifolds.

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

IMSA

Extensions in MHM and Hain's Biextension Line Bundle - Part 1

Explore complex manifolds, biextension line bundles, and normal functions in algebraic geometry. Discover formulas for Q-line bundle extensions and their topological invariants.

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

IMSA

Quantum Spectrum in Algebraic Geometry I

Explore quantum spectrum in algebraic geometry, focusing on quantum blow-up formula and its applications in birational geometry, motivic measures, and singularity resolution.

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

IMSA

The Miyaoka-Yau Equality for Pairs

Explore Miyaoka-Yau Equality for klt pairs, characterizing ball quotients through Chern classes. Gain insights into this advanced mathematical concept and its applications.

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

IMSA

Chern Classes and Indices of Vector Fields on Singular Varieties

Explore Chern classes and vector field indices on singular varieties, examining fundamental invariants in geometry and topology and their evolving theory for non-smooth spaces.

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

NCCR SwissMAP

Quillen Metrics and Applications - Part 2

Explorez les métriques de Quillen et leurs applications dans cette conférence approfondie sur les cartes jaugées, les vortex et leurs moduli.

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

Applied Algebraic Topology Network

Symmetries and Chern Classes - From Combinatorial Geometry to Algebraic and Applied Topology

Explore how Chern classes connect three mathematical areas: Tverberg-Vrećica conjecture, complex line fields on manifolds, and persistent equivariant cohomology of circles.

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

IMSA

Thom Polynomials and Their Relationships to Characteristic Classes - An Exploratory Discussion

Explore the intricate relationships between Thom polynomials, characteristic classes, and their mathematical applications through an advanced theoretical discussion of quotient Chern classes.

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

IMSA

Universally Defined Cycles

Delve into the concept of universally defined cycles for smooth varieties, exploring their relationship with Chern classes and the Franchetta conjecture extension to higher dimensions.

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

Institute for Advanced Study

On the Non-abelian Hodge Correspondence for Higher-dimensional Quasiprojective Varieties

Explore the non-abelian Hodge correspondence for higher-dimensional quasiprojective varieties, examining Simpson's homeomorphism and recent advances by Bakker, Brunebarbe and Tsimerman.

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

Institute for Advanced Study

Introduction to Non-abelian Hodge Theory

Discover Simpson's correspondence between complex local systems and semistable Higgs bundles, generalizing classical Hodge theory for smooth projective varieties.

• YouTube
• 1 hour 15 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Introduction to Non-abelian Hodge Theory

Discover Simpson's correspondence between complex local systems and semistable Higgs bundles, generalizing classical Hodge theory for smooth projective varieties.

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