Fano Varieties Courses and Certifications

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

Fields Institute

Symmetries of Fano Varieties

Explore symmetries of Fano varieties, delving into their geometric properties and mathematical significance in algebraic geometry.

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

IMSA

K-Stability of Fano Varieties

Explores K-stability of Fano varieties, connecting complex geometry and algebraic geometry. Discusses recent developments, including solved conjectures and the construction of a moduli space for Fano varieties.

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

IMSA

Smoothing Toroidal Crossing Fano Varieties Using Log Structures

Delve into advanced algebraic geometry concepts exploring the construction of log smooth Fano varieties from reflexive polytopes, focusing on smoothing techniques and log structure applications in manifold construction.

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

Harvard CMSA

The Quantum GIT Conjecture in Fano Varieties and G-Actions

Delve into advanced mathematical concepts exploring the Quantum GIT conjecture, focusing on Fano varieties, equivariant quantum cohomology, and Hamiltonian G-manifolds in algebraic geometry.

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

Instituto de Matemática Pura e Aplicada

Higher Dimensional Fano Varieties - Lecture 4

Explore higher dimensional Fano varieties in algebraic geometry. Delve into advanced concepts and recent developments in this field with expert insights from UCLA researcher Joaquín Moraga.

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

Instituto de Matemática Pura e Aplicada

Higher Dimensional Fano Varieties - Lecture 1

Explore higher dimensional Fano varieties in this advanced algebraic geometry lecture. Delve into complex mathematical concepts and theories presented by expert Joaquín Moraga from UCLA.

• YouTube
• 1 hour 24 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Machine Learning Detects Terminal Singularities in Q-Fano Varieties

Explore machine learning applications in algebraic geometry, focusing on Q-Fano varieties and terminal singularities detection. Gain insights into new combinatorial criteria and high-dimensional Q-Fano landscapes.

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

Hausdorff Center for Mathematics

Junior Trimester Program - Algebraic Geometry

Explore advanced algebraic geometry through expert lectures on modular forms, Shimura varieties, K3 surfaces, and birational geometry from leading mathematicians.

• YouTube
• 2 days 6 hours 46 minutes
• On-Demand
• Free Video

IMSA

Mixed Hodge Structures Attached to Hybrid Landau–Ginzburg Models

Explores mixed Hodge structures in Landau-Ginzburg models, focusing on functorial behavior and a new spectral sequence relating decomposed functions, with applications in mirror symmetry.

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

IMSA

Finite Generation and K-Stability

Explore recent advances in birational geometry and their impact on K-stability, including finite generation of valuations and connections to major conjectures in algebraic geometry.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

IMSA

Blow Up Formulae and Invariants II - Dimension Theory

Explore numerical invariants in meromorphic connections, their relation to singularity theory, and applications to non-rationality criteria for Fano varieties.

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

IMSA

Hodge-Theoretic Aspects of Mirror Symmetry

Explores mirror symmetry for Fano varieties through Hodge theory, discussing Hodge diamond rotation, Katzarkov--Kontsevich--Pantev conjectures, and the mirror P=W conjecture in relation to mixed Hodge structures.

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

Fields Institute

On the Mukai Conjecture and the Kostant Game

Explore the Mukai conjecture and Kostant game in algebraic geometry, delving into their connections and implications for Hamiltonian geometry.

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

IMSA

Smoothing Gorenstein Toric Singularities and Mirror Symmetry

Explore the relationship between toric variety deformations and Laurent polynomial mutations, focusing on smoothing Gorenstein singularities and their applications in mirror symmetry theory.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video