Lie Groups Courses and Certifications

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
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Lower Dimensional Betti Numbers of Homogeneous Spaces of Lie Groups

Exploration of lower dimensional Betti numbers in homogeneous spaces of Lie groups, discussing mathematical techniques and applications in algebraic topology and differential geometry.

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

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
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Holomorphic Induction of Unitary Representations of BCH Fréchet-Lie Groups

Delve into advanced mathematical concepts of holomorphic induction in infinite-dimensional Lie groups, focusing on BCH Fréchet-Lie groups and their unitary representations with positive energy conditions.

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

Institut des Hautes Etudes Scientifiques (IHES)

Homogeneous Dynamics and Geometry in Higher-Rank Lie Groups

Explore connections between homogeneous dynamics and discrete subgroups in higher-rank Lie groups, including Anosov representations and geometric structures.

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

Institut des Hautes Etudes Scientifiques (IHES)

An Introduction to Geometry and Dynamics on Semisimple Lie Groups - Lecture 3

Explore semisimple Lie groups, their structure, discrete subgroups, and asymptotic behavior through advanced mathematical concepts and theorems.

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

Mathemaniac

Lie Groups, Algebras, and Brackets - Visual Introduction to Lie Theory

Discover Lie theory through visual intuition, exploring groups, algebras, rotations in higher dimensions, exponentials, matrix operations, and the geometric meaning behind abstract concepts.

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

Insights into Mathematics

Central Polynumber Algebra and Baby Weyl Character Formula - Math Foundations 236

Explores central polynumber algebra and Weyl character formula, focusing on SU(2) and SU(3) representations. Connects to particle physics and quaternions, emphasizing polynumbers over complex exponentials.

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

Insights into Mathematics

Central Polynumbers and SL(2)/SU(2) Characters - Math Foundations 235

Explore a novel algebraic approach to SL(2) and SU(2) representation theory, emphasizing central polynumbers and mset arithmetic, with implications for Lie theory and modern physics.

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

International Centre for Theoretical Sciences

Pseudo-Reductive Groups by Brian Conrad

Explore pseudo-reductive groups with Brian Conrad, covering definitions, properties, and key theorems in this advanced mathematics lecture on algebraic group theory.

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

Insights into Mathematics

The Ubiquity of ADE Graphs, and the Mutation and Numbers Games - Math Seminars

Explore ADE graphs' mathematical significance, mutation games, and connections to advanced fields like Lie algebra, root systems, and physics in this insightful seminar on combinatorial structures.

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

Fields Institute

A Fixed-Point Formula for Dirac Operators on Lie Groupoids

Explore fixed-point formulas for Dirac operators on Lie groupoids, delving into advanced mathematical concepts and their applications in geometric analysis.

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

International Mathematical Union

Theta Correspondence and the Orbit Method

Exploring theta correspondence and orbit method in representation theory, focusing on implications for unitary representations of classical groups and special unipotent representations.

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

Fields Institute

Finite-Dimensional Representations of the Queer Lie Supergroup Q-N

Explore finite-dimensional representations of Q(n), including G-modules, Qn modules, Vera's theorem, and the typical lemma in supergeometry and bracket structures.

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

Centre de recherches mathématiques - CRM

Stationary Random Subgroups and Injectivity Radius in Negative Curvature

Explore stationary random subgroups and injectivity radius in negative curvature, focusing on rank one simple Lie groups and hyperbolic manifolds. Gain insights into recent theorems and their applications.

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