M-Seminar, Kansas State University Courses

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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video