M-Seminar, Kansas State University Courses

Perverse Coherent Sheaves on Symplectic Singularities - Part 3 of 3

Explore advanced algebraic geometry through perverse coherent sheaves on symplectic singularities, connecting modular representation theory and geometric Langlands program.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Perverse Coherent Sheaves on Symplectic Singularities - Part 2 of 3

Explore perverse coherent sheaves on symplectic singularities, connecting algebraic geometry to representation theory and gauge theories in this advanced mathematical seminar.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Moduli Spaces of Bundles on Curves with Abelian Motives

Explore the mathematical theory behind abelian motives in bundle moduli spaces, examining motivic formulas and their relationship to cohomological phenomena on curves.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Multiplicative Convolution and Double Shuffle Relations in Multiple Zeta Values

Delve into advanced mathematical concepts exploring multiple zeta values, associator relations, and regularized double shuffle relations through geometric interpretations and Hopf algebra applications.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video

Quantum Algebras, Spectral R-matrices from Equivariant Affine Grassmannians - Part 2

Delve into quantum algebras and spectral R-matrices through equivariant affine Grassmannians, exploring Niu's work on quantizations of Yang's r-matrix and their connections to 4D N=2 gauge theories.

• YouTube
• 1 hour 36 minutes
• Self-Paced
• Free Video

Orientations on Moduli Spaces of Coherent Sheaves on Calabi-Yau 4-folds - Part I

Delve into the mathematics of orientations on moduli spaces of coherent sheaves on Calabi-Yau 4-folds, exploring corrections to previous work and the concept of "flag structures" that determine canonical orientations.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

Virtual Structure on Hilbert Schemes of Affine 4-Space

Explore K-theoretic invariants of Hilbert schemes on affine 4-space, including torus localization, solid partitions, Nekrasov's formula, and connections to spin modules and origami gauge theory.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

Open Mirror Symmetry for Landau-Ginzburg Models

Delve into mirror symmetry fundamentals, exploring Saito-Givental's theory and its mirror dual through FJRW theory, with applications to Landau-Ginzburg models.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

From Quantum Loop Group to Coherent Satake Category via Fusion Product

Explore the connection between perverse coherent sheaves and quantum affine groups, examining how Feigin-Loktev fusion products bridge these mathematical structures to address the Cautis-Williams conjecture for simply-laced types.

• YouTube
• 1 hour 15 minutes
• Self-Paced
• Free Video

Counting in Calabi-Yau Categories - Part 1

Delve into homotopy cardinality replacements in Z/2-graded dg-categories, exploring Calabi-Yau structures and their applications to Hall algebras and Legendrian knot ruling polynomials.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Infinity Inner Products and Open Gromov-Witten Invariants

Delve into the construction of open Gromov-Witten potential with Sebastian Haney, exploring homotopy cyclic inner products on Fukaya A-infinity algebras and their role in extracting invariants valued in any characteristic zero field.

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

Geometry and Resurgence of WKB Solutions of Schrödinger Equations - Part 2

Delve into advanced mathematical concepts of WKB methods, quantum resurgence, and Stokes phenomenon in Schrödinger equations on compact Riemann surfaces through geometric perspectives.

• YouTube
• 1 hour 21 minutes
• Self-Paced
• Free Video

Orientations on Moduli Spaces of Coherent Sheaves on Calabi-Yau 4-folds - Part II

Delve into orientations on moduli spaces of coherent sheaves on Calabi-Yau 4-folds, exploring corrections to Cao-Gross-Joyce's work and the concept of "flag structures" determining canonical orientations.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

Moduli Spaces of Instantons and Integrable Systems - From Calogero-Moser to DELL Systems

Explore the intricate relationship between equivariant cohomology theories of instanton moduli spaces and integrable systems, focusing on Calogero-Moser, Ruijsennars-Schneider, and DELL systems.

• YouTube
• 1 hour 28 minutes
• Self-Paced
• Free Video

Geometry and Resurgence of WKB Solutions of Schrödinger Equations - Part 1

Delve into the geometric interpretation of WKB methods for Schrödinger equations, exploring quantum resurgence properties and their relationship to spectral curves and Stokes phenomena.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video