Toric Varieties Courses and Certifications

IMSA

On Some Fans and Toric Varieties Related to Branching Laws for Reductive Groups

Explore algebraic group embeddings and their representation theory through Geometric Invariant Theory, focusing on H-invariant vectors and the GIT-fan's role in encoding information.

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

IMSA

Adelic Toric Varieties and Loop Groups

Explore proalgebraic spaces, adelic abelian algebraic groups, and vector bundle categories. Discover adelic loop groups, Grassmannians, and the Birkhoff-Grothendieck theorem for holomorphic bundles.

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

Fields Institute

Toric Varieties Arising from Polygon Dissections

Explore toric varieties derived from polygon dissections, examining their geometric properties and applications in algebraic geometry and combinatorics.

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

Fields Institute

Holomorphic Torus Fibre Bundles over Toric Varieties - Generalised Calabi-Eckmann Fibrations

Explore holomorphic torus fibre bundles, Calabi-Eckmann fibrations, and complex structures on moment-angle manifolds in this advanced mathematics lecture by Taras Panov.

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

Fields Institute

Toric Varieties, Exponential Actions, Gale Duality, and Moment-Angle Manifolds

Explore toric varieties, exponential actions, Gale duality, and moment-angle manifolds in this advanced mathematics lecture by Taras Panov from Moscow State University.

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

Fields Institute

Homology of the Real Toric Varieties Associated with the Weyl Group of Types E7 and E8

Explore the homology of real toric varieties linked to E_7 and E_8 Weyl groups in this advanced mathematical talk by Seonghyeon Yu from Ajou University.

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

Fields Institute

Cohomological Homotopy Rigidity Problem for Toric Varieties

Explore the cohomological homotopy rigidity problem for toric varieties in this advanced algebraic topology lecture by Jongbaek Song from Pusan National University.

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

IMSA

Compactification of Moduli Spaces of Quantum Toric Stacks

Explores moduli spaces of quantum toric stacks and their compactification, extending toric varieties to stacky generalizations with finitely generated subgroups of R^d as "lattices".

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

Institute for Advanced Study

Discrete and Continuous Duality Algebras

Delve into Poincare duality algebras and their extensions, exploring connections to toric varieties, spherical varieties, and K-rings through homogeneous and weighted homogeneous polynomials on vector spaces and lattices.

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

Fields Institute

Introduction to Toric Vector Bundles

Explore the mathematical foundations and properties of toric vector bundles in this seminar by Christopher Manon from the University of Kentucky.

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

International Mathematical Union

Evgeny Feigin - PBW Degenerations, Quiver Grassmannians, and Toric Varieties

Explore connections between Lie theory, quiver Grassmannians, and flag variety degenerations, focusing on PBW filtration in highest weight representations and its impact on degenerate flag varieties.

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

IMSA

Rouquier Dimension Equals Krull Dimension for Toric Varieties

Explore the equality of Rouquier and Krull dimensions for toric varieties, delving into homological mirror symmetry and a multi-graded version of Hilbert's syzygy theorem.

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

Fields Institute

Equivariant K-theory of Cellular Toric Varieties and Related Spaces

Explore equivariant K-theory of cellular toric varieties and related spaces in this advanced mathematics talk by Uma Vikraman from IIT Chennai at the Fields Institute.

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

Institute for Advanced Study

Exceptional Riemann-Roch Theorems for Toric Varieties

Delve into advanced algebraic geometry concepts exploring integral isomorphisms between Chow rings and Grothendieck K-rings, with applications to toric varieties and combinatorial contexts.

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

Institute for Advanced Study

Chow Quotients of Toric and Schubert Varieties by C*-actions

Delve into advanced geometric theory exploring Chow quotients of projective varieties, toric varieties, and Schubert varieties through ℂ∗-actions, with applications in rational smoothness criteria.

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