Toric Geometry Courses and Certifications

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
• Self-Paced
• Free Video

IMSA

Nonrational Toric Geometry III - Quasifolds, Foliations, Combinatorics and One-parameter Families

Explores nonrational toric geometry through quasifolds, foliations, and combinatorics, extending classical toric geometry to new contexts and examining one-parameter families of toric quasifolds.

• YouTube
• 53 minutes
• Self-Paced
• Free Video

IMSA

Nonrational Toric Geometry I - Symplectic Toric Quasifolds Minicourse

Explore symplectic toric quasifolds, generalizing toric varieties to non-rational polytopes. Learn about quasilattices, quasirationality, and quasitori through examples like quasispheres and Penrose tilings.

• YouTube
• 53 minutes
• Self-Paced
• 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
• Self-Paced
• Free Video

IMSA

An Introductory Mini Course into Quantum Toric Geometry Lecture I - Day 1

Explore quantum toric geometry, a non-commutative generalization of toric geometry. Learn about stacks, quantum tori, and quantum toric varieties, building on foundations of traditional toric geometry.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• 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
• Self-Paced
• Free Video

IMSA

Ernesto Lupercio- Quantum Toric Geometry Pt. II

Explores quantum toric geometry, generalizing toric geometry with moduli spaces. Advanced mathematical concepts for researchers in algebraic topology, geometry, and mathematical physics.

• YouTube
• 57 minutes
• Self-Paced
• 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
• Self-Paced
• Free Video

IMSA

Hodge Numbers in Quantum Toric Geometry

Explore Quantum Toric Geometry and its impact on Hodge numbers in non-algebraic complex manifolds. Discover enriched perspectives in this collaborative research presentation.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

IMSA

Hodge Structures and Quantum Toric Geometry

Explore Quantum Toric Geometry and its impact on Hodge Theory generalizations in this advanced mathematics colloquium, featuring insights from collaborative research in non-commutative spaces.

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

Fields Institute

Toric Matroid Bundles - Algebraic Geometry and Combinatorics

Explore toric matroid bundles with Christopher Manon, delving into advanced mathematical concepts and their applications in toric topology and geometry.

• YouTube
• 39 minutes
• Self-Paced
• Free Video

IMSA

Nonrational Toric Geometry II - Quasifolds, Foliations, Combinatorics and One-parameter Families

Explore complex toric quasifolds, their structure, and relation to rational toric varieties. Learn about extending constructions to nonsimple convex polytopes in symplectic and complex settings.

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

IMSA

Ernesto Lupercio: Quantum Toric Geometry

Explore quantum toric geometry, a generalization of toric geometry analogous to how quantum torus extends the usual torus. Delve into quantum toric varieties and their moduli spaces.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

IMSA

Discriminants and Toric Birational Geometry

Explore Gorenstein toric singularities, B-side categories in toric homological mirror symmetry, and GKZ hypergeometric D-modules. Discover the conjectural construction of associated spherical functors.

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