M-Seminar, Kansas State University Courses

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 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

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

Perverse Coherent Sheaves on Symplectic Singularities - Part 1 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 4 minutes
• Self-Paced
• Free Video

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

The Gauss-Manin Connection in Noncommutative Geometry

Explore the Gauss-Manin connection in noncommutative geometry, where varieties become associative rings and De Rham cohomology transforms into periodic cyclic complexes.

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

Hyperbolic Localization in Donaldson-Thomas Theory - Part 1 of 3

Explore hyperbolic localization functors in Donaldson-Thomas theory, connecting Białynicki-Birula decompositions with vanishing cycles on Calabi-Yau threefold moduli spaces.

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

Hyperbolic Localization in Donaldson-Thomas Theory - Part 3 of 3

Explore hyperbolic localization in Donaldson-Thomas theory, covering vanishing cycles, shifted symplectic geometry, and wall-crossing formulas for Calabi-Yau threefolds.

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

Hyperbolic Localization in Donaldson-Thomas Theory - Part 2 of 3

Explore hyperbolic localization in Donaldson-Thomas theory, focusing on perverse sheaves and critical loci of functions on Calabi-Yau threefold moduli spaces.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Abelian Hall Categories - Part 3 of 3

Explore advanced categorical structures that categorify K-theoretic Hall algebras through finite length abelian categories, focusing on canonical bases and quantum toroidal algebras.

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

Abelian Hall Categories - Part 2 of 3

Explore how quivers generate finite length abelian categories that categorify K-theoretic Hall algebras, with simples forming canonical bases for quantum toroidal algebras.

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

Abelian Hall Categories - Part 1 of 3

Explore how quivers generate finite length abelian categories that categorify K-theoretic Hall algebras, with simples forming dual canonical bases for quantum toroidal algebras.

• YouTube
• 1 hour 27 minutes
• Self-Paced
• Free Video

Frobenius Structures for Quantum Differential and Q-Difference Equations - Lecture 1

Explore Frobenius structures connecting Kloosterman sums to quantum differential equations in Nakajima varieties, with applications to mirror symmetry and p-adic theory.

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

Frobenius Structures for Quantum Differential and Q-Difference Equations - Lecture 3

Explore Frobenius structures connecting Kloosterman sums to quantum differential equations in Nakajima varieties, with applications to mirror symmetry and p-adic theory.

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