M-Seminar, Kansas State University Courses

Symplectic Orbifold Gromov-Witten Invariants

Dive into symplectic orbifold Gromov-Witten invariants, exploring recent developments in moduli spaces and global Kuranishi charts for pseudo-holomorphic curves in symplectic orbifolds.

• YouTube
• 1 hour 12 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

Superabundance and Unobstructedness in Lagrangian Torus Fibrations - Lecture

Explore Lagrangian realizations of tropical curves in torus fibrations, focusing on non-superabundance and unobstructedness in 3D settings.

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

Cohomological Hall Algebra of Cyclic Quivers and Integral Form of Affine Yangians

Explore cohomological Hall algebras of cyclic quivers and their connection to affine Yangians, using tools from Donaldson-Thomas theory and moduli spaces.

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

The Exponential Type Conjecture for Quantum Connections

Delve into quantum connections and formal singularity types, exploring the exponential type conjecture proof for closed monotone symplectic manifolds through mod p arguments and Katz's theorem.

• YouTube
• 1 hour 6 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

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

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

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

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

Categorical and Geometric Enumerative Invariants

Explore categorical enumerative invariants for Calabi-Yau categories and their chain-level CohFT structures, connecting Fukaya categories with symplectic manifold geometry.

• YouTube
• 1 hour 12 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

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

Quantum Algebras and Spectral R-matrices from Equivariant Affine Grassmannians - Part 1

Delve into quantum algebras and spectral R-matrices through equivariant affine Grassmannian geometry, exploring connections to holomorphic-topological twist of 4D N=2 gauge theories.

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

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

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

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