Representation Theory Courses and Certifications

Institute for Advanced Study

Representation Theory & Combinatorics of the Symmetry Group and Related Structures - Monica Vazirani

Explore symmetry group representation theory and combinatorics, focusing on cycle notation, permutations, and linearization techniques for advanced mathematical analysis.

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

Institute for Advanced Study

Representations of P-Adic Groups and Applications - Jessica Fintzen

Explore p-adic group representations, supercuspidal representations, and their applications in number theory with Jessica Fintzen's in-depth seminar on advanced mathematical concepts.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Marie-France Vigneras - Representations of GLn(D) Near the Identity

Explore representations of general linear groups over p-adic fields, focusing on dimension formulas for fixed points under congruence subgroups and extensions to inner forms.

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

Hausdorff Center for Mathematics

J. E. Rodriguez Camargo: A Local Jacquet-Langlands Correspondence for Locally Analytic D-Modules

Explore an equivalence between GL₂(F)-equivariant D-modules on Drinfeld space and D*^-equivariant D-modules on P¹, with applications to Scholze's functor and admissible representations.

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

Hausdorff Center for Mathematics

Generic Character Sheaves for Parahoric Subgroups

Exploration of Lusztig's character sheaves theory, extending to positive-depth cases and addressing Lusztig's conjecture. Focuses on perverse sheaves and parahoric Deligne-Lusztig induction in representation theory.

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

International Centre for Theoretical Sciences

Stratification and Duality for Representations of Finite Groups - Lecture 3

Explore advanced concepts in finite group representation theory, focusing on stratification and duality principles. Gain insights into algebraic structures and their applications in mathematics.

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

International Centre for Theoretical Sciences

Stratification and Duality for Representations of Finite Groups - Lecture 2

Explore advanced concepts in finite group representation theory, focusing on stratification and duality principles. Gain insights into algebraic structures and their applications in mathematics.

• YouTube
• 1 hour 25 minutes
• On-Demand
• Free Video

Simons Institute

Representation Theory in TCS and Extremal Combinatorics

Explore how Representation Theory extends Boolean function theory, leading to new insights in theoretical computer science and extremal combinatorics.

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

Hausdorff Center for Mathematics

Explicit Examples of Categorical Local Langlands

Explore explicit examples of categorical local Langlands, focusing on GL_2 and SL_2 groups, examining fully faithful functors, sheaf computations, and connections to Langlands classification.

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

International Centre for Theoretical Sciences

Harish-Chandra Tempered Representations and Homogeneous Spaces by Yves Benoist

Explore Harish-Chandra tempered representations and homogeneous spaces with Yves Benoist in this interactive lecture. Engage with the speaker and deepen your understanding of advanced mathematical concepts.

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

International Mathematical Union

Representations of Reductive Groups Over Local Fields

Explore reductive group representations over local fields with Tasho Kaletha, delving into advanced mathematical concepts and their applications in algebraic number theory.

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

International Mathematical Union

Joel Kamnitzer- Perfect Bases in Representation Theory- Three Mountains and Their Springs

Exploration of perfect bases in representation theory, examining three approaches and their combinatorial implications for tensor product multiplicities in semisimple groups.

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

International Centre for Theoretical Sciences

Stratification and Duality for Representations of Finite Groups - Lecture 4

Explore finite group representations through stratification and duality concepts. Delve into advanced algebraic techniques and their applications in modular representation theory.

• YouTube
• 1 hour 53 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

A Categorified Double Centraliser Theorem and Applications to Soergel Bimodules

Explore advanced representation theory concepts, including categorified double centraliser theorem and its applications to Soergel bimodules in finite Coxeter type and characteristic zero.

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

Hausdorff Center for Mathematics

Monica Vazirani- Representations of the Affine BMW Category

Explore Walker's TQFT-motivated construction of affine BMW category representations, their combinatorial description, and implications for affine BMW algebra representations in this advanced mathematics lecture.

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