BunG Seminar Courses

Chiral Algebras and the Feigin-Frenkel Duality at Critical Level

Delve into advanced mathematical concepts exploring vertex algebras, chiral algebras, and Feigin-Frenkel duality, with applications to geometric Langlands program and factorization algebras.

• YouTube
• 2 hours 3 minutes
• Self-Paced
• Free Video

The Arkhipov-Bezrukavnikov Equivalence and Categorifications of the Anti-Spherical Module

Delve into advanced algebraic geometry exploring the Arkhipov-Bezrukavnikov equivalence, examining three distinct categorifications of the anti-spherical module and their relationships through sheaf theory.

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

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

Soergel Functors in Geometric Representation Theory - Recent Developments

Delve into advanced geometric representation theory, exploring Soergel functors and their applications in describing complex categories through simpler module structures and Hecke categories.

• YouTube
• 2 hours 2 minutes
• Self-Paced
• Free Video

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

The Arkhipov-Bezrukavnikov-Ginzburg Equivalence in Quantum Group Representations - Lecture 56

Delve into advanced mathematical concepts exploring the relationships between quantum groups, coherent sheaves, and perverse sheaves through the lens of the ABG equivalence theorem.

• YouTube
• 1 hour 53 minutes
• Self-Paced
• Free Video

Local Relative Langlands Conjecture - BunG Seminar LV

Delve into the local relative Langlands conjecture with Daniil Klyuev, exploring hyperspherical varieties, dual constructions, and category equivalences between G-equivariant sheaves and modules over cohomological shifts.

• YouTube
• 1 hour 47 minutes
• Self-Paced
• Free Video

Introduction to Vertex Algebras - From Heisenberg to Virasoro Algebras

Delve into vertex algebras, exploring Heisenberg, Kac-Moody, and Virasoro structures while understanding their connections to affine W-algebras and Zhu algebra fundamentals.

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

Representation Theory for Finite W-algebras

Delve into advanced representation theory, exploring Whittaker reduction, finite W-algebras, and their connection to Lie algebras through geometric and algebraic perspectives.

• YouTube
• 1 hour 33 minutes
• Self-Paced
• Free Video

Construction of Finite W-algebras and Slodowy Slice Quantization

Delve into advanced mathematical concepts of Slodowy slices, nilpotent orbits, and finite W-algebras, exploring their construction, Poisson structures, and quantization methods in semisimple Lie algebras.

• YouTube
• 1 hour 23 minutes
• Self-Paced
• Free Video

Shtukas and Excursions in Categorical Spectral Theory - Talk 42

Delve into advanced mathematical concepts exploring the relationship between excursion operators, shtuka cohomologies, and categorical spectral action through categorical traces.

• YouTube
• 2 hours 17 minutes
• Self-Paced
• Free Video

The Global Hecke Action - Talk 41

Delve into geometric Satake theory and explore how Rep(G^vee) actions on BunG sheaves integrate into global Hecke modifications, with applications in Betti, de Rham, and étale settings.

• YouTube
• 1 hour 48 minutes
• Self-Paced
• Free Video

Moduli Spaces of Local Systems in Algebraic Varieties

Delve into advanced mathematical concepts of local systems and Galois representations, exploring construction methods and parameter spaces in Betti, deRham, and l-adic settings.

• YouTube
• 1 hour 57 minutes
• Self-Paced
• Free Video

Singular Support for Constructible Sheaves in Étale Topology

Delve into advanced mathematical concepts of singular support in constructible sheaves, exploring wave front distributions and étale versions for geometric Langlands theory.

• YouTube
• 2 hours 6 minutes
• Self-Paced
• Free Video

Basics of Derived Algebraic Geometry - Talk 38

Dive into fundamental concepts of derived algebraic geometry, exploring prestacks, tangent complexes, quasi-smooth derived schemes, and ind-coherent sheaf singular support analysis.

• YouTube
• 2 hours 3 minutes
• Self-Paced
• Free Video