Lie Groups Courses and Certifications

Stony Brook Mathematics

Uniform Volume Doubling and Functional Inequalities on Lie Groups

Explore functional inequalities on Lie groups, focusing on uniform volume doubling and its implications for SU(2) and related structures. Gain insights into heat kernel estimates and measure contracting properties.

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

Stony Brook Mathematics

Positivity, Representations, and Non-Commutative Hyperbolic Geometry

Explore total positivity in matrices, its generalization to split real Lie groups, and a new notion of positivity in flag varieties with applications to higher Teichmüller spaces.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Local Mixing of Diagonal Flows on Anosov Homogeneous Spaces

Explore local mixing of diagonal flows on Anosov homogeneous spaces, generalizing Winter's result and discussing applications in equidistribution and matrix coefficients.

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

Institut des Hautes Etudes Scientifiques (IHES)

Logarithmic Sobolev Inequalities on Homogeneous Spaces

Explore logarithmic Sobolev inequalities on homogeneous spaces with sub-Riemannian structures. Discover how constants depend on Lie group geometry and remain independent of dimension in certain cases.

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

Fields Institute

Lie Groups and Quantization - Lecture 11

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

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

Fields Institute

Lie Groups and Quantization - Lecture 7

Delve into advanced mathematical concepts exploring Lie groups and quantization theory, focusing on their fundamental principles and applications in graduate-level mathematics.

• YouTube
• 1 hour 19 minutes
• On-Demand
• Free Video

Fields Institute

Lie Groups and Quantization - Lecture 10

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

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

Fields Institute

Lie Groups and Quantization - Lecture 12

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

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

Fields Institute

Lie Groups and Quantization - Lecture 2

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

• YouTube
• 1 hour 21 minutes
• On-Demand
• Free Video

Fields Institute

Lie Groups and Quantization - Lecture 5

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

• YouTube
• 1 hour 21 minutes
• On-Demand
• Free Video

Fields Institute

Lie Groups and Quantization - Lecture 6

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

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

Fields Institute

Lie Groups and Quantization - Lecture 4

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

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

Fields Institute

Lie Groups and Quantization - Lecture 3

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

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

Fields Institute

Lie Groups and Quantization - Lecture 1

Delve into fundamental concepts of Lie groups and their applications in quantization through advanced mathematical exploration and theoretical frameworks in graduate-level mathematics.

• YouTube
• 1 hour 22 minutes
• On-Demand
• Free Video

Fields Institute

Lie Groups and Quantization - Lecture 15

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

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video