Lie Theory Courses and Certifications

IMSA

Complex and Symplectic Structures on Almost Abelian Lie Groups

Delve into the classification of left-invariant complex and symplectic structures on almost abelian Lie groups, exploring mathematical research developments in solvable Lie group geometry.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Central Extensions in Infinite-Dimensional Geometry - Theory and Applications

Explore advanced mathematical concepts of central Lie algebra extensions, focusing on integration methods for current groups and diffeomorphism groups in infinite-dimensional settings.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Banach-Lie Groupoids in Infinite-dimensional Geometry - Part 2

Delve into advanced mathematical concepts of Banach-Lie groupoids, exploring theoretical frameworks and applications in infinite-dimensional geometry.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Banach-Lie Groupoids in Infinite-dimensional Geometry - Part 1

Dive into the mathematical foundations of Banach-Lie groupoids, exploring their theoretical framework and applications in infinite-dimensional geometry.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Principal Bundle Groupoids versus Vector Bundle Groupoids in Differential Geometry

Delve into the mathematical correspondence between vector bundle groupoids and principal bundle groupoids, exploring frame bundles, Lie groupoids, and their geometric applications.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Lie Algebras of Diffeomorphism Groups of Non-compact Manifolds - Part 1

Delve into advanced mathematical concepts exploring diffeomorphism groups of non-compact manifolds, focusing on their Lie algebra structures and elastic properties in diffeological spaces.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Fields Institute

Lie Groups and Quantization - Lecture 20

Delve into advanced mathematical concepts exploring Lie groups and quantization theory, focusing on their interconnections and applications in theoretical physics and geometry.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Fields Institute

Lie Groups and Quantization - Lecture 18

Delve into advanced mathematical concepts of Lie groups and their applications in quantization theory through rigorous exploration of fundamental principles and theorems.

• YouTube
• 1 hour 15 minutes
• Self-Paced
• Free Video

Fields Institute

Lie Groups and Quantization - Lecture 17

Delve into advanced mathematical concepts of Lie groups and their applications in quantization theory through rigorous theoretical exploration and practical examples.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

Fields Institute

Lie Groups and Quantization - Lecture 16

Delve into advanced mathematical concepts exploring Lie groups and quantization theory, focusing on their interconnections and applications in theoretical physics and geometry.

• YouTube
• 1 hour 15 minutes
• Self-Paced
• Free Video

Fields Institute

Lie Groups and Quantization - Lecture 21

Delve into advanced mathematical concepts exploring Lie groups and their applications in quantization theory through rigorous theoretical frameworks and practical examples.

• YouTube
• 1 hour 15 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Inequalities Defining Polyhedral Realizations and Monomial Realizations in Crystal Bases

Delve into advanced crystal bases theory, exploring polyhedral and monomial realizations in Lie algebras, with focus on inequalities defining convex cones and Laurent monomial expressions.

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

International Centre for Theoretical Sciences

Symmetric Polynomials of the Weights of a Lie Group Representation

Delve into advanced concepts of symmetric polynomials and their relationship to Lie group representation weights, exploring fundamental mathematical structures and their applications.

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

INI Seminar Room 2

Okounkov's Conjecture via BPS Lie Algebras

Delve into Okounkov's conjecture and its proof through BPS Lie algebras, exploring connections between Yangian algebras, quiver varieties, and Kac polynomials in algebraic geometry.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Banach-Lie Groupoids - Part 3

Delve into advanced mathematical concepts of Banach-Lie groupoids, exploring theoretical frameworks and applications in infinite-dimensional geometry through expert analysis.

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