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 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

Mock Modularity of Calabi-Yau Threefolds - Part 2 of 3

Explore modular properties of rank 0 Donaldson-Thomas invariants and their generating functions as mock modular forms for Calabi-Yau threefolds.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video

Mock Modularity of Calabi-Yau Threefolds - Part 1 of 3

Explore modular forms, mock modular forms, and Jacobi forms while discovering generalized Donaldson-Thomas invariants for Calabi-Yau threefolds in advanced mathematical physics.

• YouTube
• 1 hour 9 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

Motivic Classes of Varieties and Stacks with Applications to Higgs Bundles and More

Explore motivic classes of varieties and stacks, from point counting over finite fields to explicit formulas for moduli of Higgs bundles and connections.

• YouTube
• 1 hour 13 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

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

Frobenius Structures for Quantum Differential and Q-Difference Equations - Lecture 2

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
• Self-Paced
• Free Video

Remodeling Conjecture with Descendants

Explore advanced mathematical connections between Gromov-Witten invariants and Topological Recursion in toric Calabi-Yau manifolds through mirror symmetry theory.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

BPS Cohomology and Quasi-BPS Categories - Lecture 1 of 4

Explore BPS cohomology and quasi-BPS categories for symmetric stacks, focusing on quivers with potential and Higgs bundles on curves through advanced algebraic geometry.

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

Mock Modularity of Calabi-Yau Threefolds - Part 3 of 3

Explore advanced techniques for computing polar terms in mock modular forms encoding rank 0 Donaldson-Thomas invariants using wall-crossing and topological string integration.

• YouTube
• 1 hour 16 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