Grassmannians Courses and Certifications

Inside Livermore Lab

Model Reduction via Optimization of Projection Operators and Reduced-Order Dynamics

Explore non-intrusive methods for computing reduced-order models, focusing on systems with large-amplitude transient growth. Learn techniques to identify oblique projection operators and reduced-order dynamics from data.

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

Institute for Advanced Study

Tropical Quiver Representations and Their Geometric Applications

Delve into advanced algebraic geometry concepts through tropical quiver representations, exploring Grassmannians, flag varieties, and their matroidal analogues as fundamental moduli spaces.

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

Centre International de Rencontres Mathématiques

Frieze Patterns and Representation Theory

Explore connections between frieze patterns and representation theory, from Conway-Coxeter friezes to higher dimensional SLk friezes and their applications to cluster algebras.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Harvard CMSA

Positive Grassmannian and Cluster Algebras I

Explore the mathematical foundations of positive Grassmannian varieties and their deep connections to cluster algebra structures in this advanced lecture.

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

Harvard CMSA

Positive Grassmannian and Cluster Algebras III

Explore advanced connections between positive Grassmannian varieties and cluster algebras in this specialized mathematical lecture from Harvard CMSA's summer school.

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

Harvard CMSA

Positive Grassmannian and Cluster Algebras II

Explore advanced connections between positive Grassmannian geometry and cluster algebra structures in this specialized mathematical lecture from Harvard CMSA's summer school series.

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

Harvard CMSA

Definitions and First Examples of Positive Geometries II

Explore fundamental concepts and initial examples of positive geometries in this advanced mathematical framework connecting total positivity with quantum field theory applications.

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

Institute for Advanced Study

Quilts of Alternating Sign Matrices - From Boolean Lattices to Distributive Structures

Explore the mathematical theory of alternating sign matrix quilts, their connections to rank functions, Boolean lattices, and Schubert varieties, with applications in enumerative geometry.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Institute for Advanced Study

The Picard Group of a Cominuscule Richardson Variety

Delve into advanced algebraic geometry concepts exploring Richardson varieties in cominuscule Grassmannians, focusing on Picard group properties and their relationship to skew diagrams and Chow groups.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Institute for Advanced Study

Mirror Symmetry for the Grassmannian and Its Schubert Varieties

Delve into advanced mirror symmetry concepts for Grassmannian Schubert varieties, exploring superpotential theory, toric degenerations, and quantum cohomology applications in algebraic geometry.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• 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
• Self-Paced
• Free Video

Harvard CMSA

Orthogonality of Spin q-Whittaker Polynomials

Delve into the orthogonality of spin q-Whittaker polynomials, exploring their properties as symmetric polynomials, eigenrelations, and applications to directed random polymer models with Beta weights.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Institute for Advanced Study

Buildings, Galleries and Beyond

Explore Bruhat-Tits buildings, their combinatorial toolkits, and relationships to groups, Grassmannians, flag varieties, and Coxeter group combinatorics.

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

International Centre for Theoretical Sciences

Complete Monotonicity and Dual Volumes of Positive Geometries - Lecture 1

Delve into the mathematical foundations of positive geometries in scattering amplitudes, exploring complete monotonicity and dual volumes in this advanced theoretical physics lecture.

• YouTube
• 1 hour 27 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Doubling Our Positivity With Double Copy Part II: Loops - Lecture 2

Delve into advanced concepts of Double Copy theory at loop level with John Joseph Carrasco, exploring mathematical connections between scattering amplitudes and cosmological correlators.

• YouTube
• 1 hour 38 minutes
• Self-Paced
• Free Video