Toric Varieties Courses and Certifications

IMSA

Non-Simplicial Quantum Toric Varieties

Explore the construction of quantum toric varieties linked to arbitrary fans on finitely generated subgroups of R^d, expanding mathematical understanding in algebraic geometry.

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

IMSA

Irrational Toric Varieties and the Secondary Polytope

Explore irrational toric varieties, their connections to classical theory, and their relationship with secondary polytopes in algebraic geometry and combinatorics.

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

IMSA

Is There Geometric Recursion for the Moduli Space of Toric Varieties?

Explore moduli space of quantum toric varieties, drawing parallels with geometric recursion. Delve into quantum lattices, tori, and CP1, examining group actions, calibration, and quantum geometric invariant theory.

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

IMSA

Cluster Varieties, Toric Degenerations and Convexity in Algebraic Geometry

Explore the geometric approach to cluster varieties, examining toric degenerations and convexity principles in relation to minimal models and the Gross-Siebert mirror symmetry program.

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

IMSA

Deformations and Mutations of Affine Gorenstein Toric Varieties

Explore the correspondence between one-parameter deformations of affine Gorenstein toric varieties and mutations of Laurent polynomials with Newton polytopes.

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

IMSA

Mutations and Deformations of Gorenstein Toric Varieties via Log Resolutions

Explore mutations and deformations of Gorenstein toric varieties through logarithmic geometry, connecting mirror symmetry concepts with new mathematical approaches.

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

Fields Institute

Symplectic Geometry

Master symplectic manifolds, Darboux theorem, Hamiltonian mechanics, moment maps, and advanced topics like toric varieties, quantization, and mirror symmetry in this comprehensive mathematical framework.

• YouTube
• 1 day 11 hours 57 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

Institut des Hautes Etudes Scientifiques (IHES)

Introduction to Resurgence via Wall-crossing Structures - Lecture 1

Explore an alternative approach to Borel-Écalle resummation using analytic wall-crossing structures. Delve into holomorphic bundles, gauge transformations, and geometric interpretations with practical examples.

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

ICTP Mathematics

Cluster Algebras and Mirror Symmetry - Lecture 1

Explore the intricate connection between cluster algebras and mirror symmetry in mathematics, delving into advanced concepts and their applications in algebraic geometry.

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

IMSA

Homological Mirror Symmetry - Progress in Quantum Toric Geometry

Explore recent developments in quantum toric geometry, moduli spaces of toric varieties, and their conjectural links to birational geometry, drawing from cutting-edge research in the field.

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

IMSA

An Introductory Mini Course into Quantum Toric Geometry Lecture II

Explore quantum toric geometry, including LVM theory, quantum GIT, and moduli spaces of toric varieties. Delve into non-commutative spaces and their relation to traditional toric geometry.

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

IMSA

Log Symplectic Pairs and Mixed Hodge Structures

Explores log symplectic pairs, their connection to hyperkaehler variety degenerations, and classification of pure weight pairs. Discusses analogies with log Calabi-Yau surfaces and implications for mixed Hodge structures.

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

IMSA

Enumerative Geometry and the Quantum Torus

Explore enumerative geometry through tropical curves, pseudotropical curves, and their connection to Lie algebras and quantum torus. Discover innovative approaches to classical counting problems in algebraic geometry.

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

IMSA

Quantum Toric Geometry I

Explore quantum toric geometry, a generalization of classical toric geometry using quantum tori, allowing for irrational fans. Learn foundations and motivations behind this advanced mathematical concept.

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