Fano Manifolds Courses and Certifications

Centre International de Rencontres Mathématiques

A Family of Fano Manifolds Obtained as Linear Sections of the Spinor Tenfold

Explore the rich geometry of Fano manifolds through linear sections of the spinor tenfold, connecting E8 Lie algebras, graded structures, and classical Kummer quartic surfaces.

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

International Mathematical Union

Xiaohua Zhu - Kähler-Ricci Flow on Fano Manifolds

Explore the Kähler-Ricci flow on Fano manifolds, delving into complex geometry and differential equations. Gain insights into this advanced mathematical topic through expert analysis and explanations.

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

BIMSA

Kahler-Einstein Metrics on Fano Manifolds - ICBS 2024

Explore Kahler-Einstein metrics on Fano manifolds, bridging differential and algebraic geometry through singularity formations and recent advancements in the field.

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

Institute for Advanced Study

Mirror Symmetry for Open Gromov-Witten Invariants of Fano Manifolds

Explore mirror symmetry through matrix factorizations and their correspondence to Lagrangian submanifolds in Fano manifolds using non-Archimedean frameworks.

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

Instituto de Matemática Pura e Aplicada

Fano Manifolds and the Lefschetz Defect - Class 4

Explore Fano manifolds and Lefschetz defect in this advanced algebraic geometry lecture. Gain insights into complex mathematical concepts and their applications in modern research.

• YouTube
• 1 hour 26 minutes
• On-Demand
• Free Video

Instituto de Matemática Pura e Aplicada

Fano Manifolds and the Lefschetz Defect - Class 1

Explore Fano manifolds and Lefschetz defect in algebraic geometry. Delve into advanced concepts with expert Cinzia Casagrande in this comprehensive mini-course from the V Latin American School of Algebraic Geometry.

• YouTube
• 1 hour 25 minutes
• On-Demand
• Free Video

IMSA

SYZ for Hypersurfaces of Toric Fano Manifolds and Optimal Transport - Part 1

Delve into the relationship between SYZ-conjecture, Calabi-Yau hypersurfaces, and optimal transport theory through advanced mathematical analysis of Monge-Ampère equations and toric geometry.

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

IMSA

SYZ for Hypersurfaces of Toric Fano Manifolds and Optimal Transport - Part 2

Delve into advanced mathematical concepts exploring SYZ conjecture, Calabi-Yau hypersurfaces, and optimal transport theory through real Monge-Ampère equations and toric Fano manifolds.

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

Instituto de Matemática Pura e Aplicada

Fano Bott Manifolds and Contact Invariants of Their Gorenstein Prequantizations

Explore Fano Bott manifolds and contact invariants of their Gorenstein prequantizations in this advanced mathematical lecture from a leading symplectic geometry expert.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

IMSA

Higher Fano Manifolds in Algebraic Geometry

Explore higher Fano manifolds in algebraic geometry, their properties, and recent developments. Learn about positivity of higher Chern characters and research on homogeneous and toric higher Fano manifolds.

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

IMSA

Fixed Loci of Anti-Symplectic Involutions

Explore geometric constructions linking Fano manifolds and hyperkähler manifolds, focusing on reversing the process to recover Fano manifolds from hyperkähler structures.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

IMSA

Special Lecture Series on Numerical Geometry - Tristan Collins

Explore complete Calabi-Yau metrics on Fano manifolds with singular divisors, focusing on two-component cases and discussing potential generalizations to more complex scenarios.

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

IMSA

The Quantum Connection and Its Mod p Reductions

Delve into advanced mathematical concepts exploring quantum connections on Fano manifolds, focusing on Steenrod-type quantum operations and recent structural developments.

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

Institute for Advanced Study

A Toric Case of the Thomas-Yau Conjecture

Explore the Thomas-Yau conjecture for Lagrangian sections in Calabi-Yau fibrations, proving equivalence between Hamiltonian isotopy and stability conditions via Fukaya-Seidel categories.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

BIMSA

The Rich World of Fano Geometry

Explore the fascinating realm of Fano geometry through expert insights from renowned mathematician Caucher Birkar in this comprehensive mathematical lecture.

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