Representation Theory Courses and Certifications

Institute for Mathematical Sciences

Models of the Heisenberg Weil Representation and the Metaplectic Group - Part 1

Delve into advanced mathematical concepts exploring Weil representation, Metaplectic group theory, and Weil index through detailed examinations of the local Theta correspondence.

• YouTube
• 1 hour 25 minutes
• Self-Paced
• Free Video

INI Seminar Room 2

Representation Categories and Motives

Explore representation categories and motives with Professor Markus Spitzweck in this mathematical seminar from the Equivariant homotopy theory in context event at the Isaac Newton Institute.

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

Institute for Advanced Study

Equalities and Inequalities on Products of Schur Functions

Delve into the mathematical exploration of Schur functions, Littlewood-Richardson coefficients, and conditions for Schur positivity in symmetric function theory with Daniel Soskin.

• YouTube
• 1 hour 31 minutes
• Self-Paced
• Free Video

BunG Seminar

Geometrization of Hecke Algebras - Seminar LIV

Delve into advanced mathematical concepts exploring affine Hecke algebras, their geometrization through Steinberg varieties, and connections to the geometric local Langlands program.

• YouTube
• 1 hour 40 minutes
• Self-Paced
• Free Video

Cambridge University Press

Regular Schur Labeled Skew Shape Posets and Their 0-Hecke Modules

Explore Young-Hun Kim's research on Regular Schur labeled skew shape posets and their 0-Hecke modules in this academic presentation of mathematical concepts published in Forum of Mathematics.

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

Cambridge University Press

Quantum Wreath Products and Schur–Weyl Duality I

Delve into quantum wreath products and Schur-Weyl duality with researcher Chun-Ju Lai as he presents the mathematical foundations behind his co-authored academic paper published in Forum of Mathematics.

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

BIMSA

Derived Equivalences from Invariant Theory

Explore derived equivalences in algebraic geometry through invariant theory, focusing on homological algebra and category theory applications to study varieties with insights from physics and noncommutative algebra.

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

Harvard CMSA

U-Equations from Finite Dimensional Algebras - Applications in Cluster Algebras and Amplitudes

Explore finite dimensional algebra systems and their applications in representation theory, focusing on u-equations, tau-tilting theory, and connections to cluster algebras and amplitudes.

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

Harvard CMSA

From Affine Hecke Category to Invariant Distributions

Delve into advanced mathematical concepts exploring affine Hecke categories, invariant distributions, and their applications in harmonic analysis through geometric realizations and Lusztig's asymptotic algebra.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Harvard CMSA

The Tame Categorical Local Langlands Correspondence

Delve into advanced mathematical concepts exploring the tame categorical local Langlands correspondence, focusing on p-adic groups and depth zero supercuspidal representations.

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

Harvard CMSA

Combinatorics of Principal W-algebras of Type A

Delve into advanced combinatorial mathematics exploring principal W-algebras, cylindric partitions, and their connection to torus knots through fermionic character expressions and Bailey machinery.

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

Harvard CMSA

Rationality for a Large Class of Affine W-algebras

Delve into advanced representation theory concepts, exploring rationality in affine W-algebras and their connection to modular tensor categories in vertex operator algebras.

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

Harvard CMSA

Quantizations of Nilpotent Orbits and Their Lagrangian Subvarieties

Delve into advanced mathematical concepts exploring quantizations of nilpotent orbits and their relationship with Lagrangian subvarieties in representation theory.

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

Harvard CMSA

Tensor Structures Associated to the N=1 Super Virasoro Algebra

Explore tensor structures and braided tensor categories in N=1 super Virasoro algebra representations, focusing on rigidity properties at specific central charges.

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

BunG Seminar

W-algebras and Whittaker Categories - Talk 51

Delve into advanced mathematical concepts exploring W-algebras, Whittaker categories, and Kac-Moody algebras, with applications in affine Skryabin theorem and categorical Feign Frenkel duality.

• YouTube
• 1 hour 41 minutes
• Self-Paced
• Free Video