BunG Seminar Courses

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

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

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

Semi-infinite Cohomology and BRST Complex in W-algebras

Delve into advanced mathematical concepts of semi-infinite cohomology, exploring W-algebras through BRST resolution and discovering connections to Tate Lie algebra and Zhu's algebra theory.

• YouTube
• 1 hour 53 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

Shtukas and Global Langlands for Function Fields - Talk 37

Delve into V. Lafforgue's groundbreaking proof of global Langlands correspondence, exploring shtukas, geometric Satake, and excursion operators in function fields through expert analysis.

• YouTube
• 2 hours 7 minutes
• Self-Paced
• Free Video

Overview of Restricted Geometric Langlands Theory

Delve into categorical formulations of geometric Langlands theory, exploring restricted local systems, their applications in arithmetic, and connections to automorphic forms through Frobenius traces.

• YouTube
• 2 hours 5 minutes
• Self-Paced
• Free Video

Counting Points on Bun_G - Talk 35

Delve into advanced algebraic geometry as Matthew Emerton explores G-L trace formula for Bun_G, providing a detailed proof of Conjecture 8 from Lurie's earlier lectures.

• YouTube
• 1 hour 46 minutes
• Self-Paced
• Free Video