IMSA Courses

Coinduction for Comodule Algebras

1 rating

Explore coinduction for comodule algebras, focusing on constructing C_c(G)-comodule algebras from C(H)-comodule algebras for finite H, and its implications for crossed products and group cases.

• YouTube
• 44 minutes
• Self-Paced
• Free Video

Interpolation for Polynomials in Two Variables

1 rating

Explore advanced polynomial interpolation techniques in two variables, covering dimension counts, Picard groups, and conjectures like Segre's and Nagata's. Delve into cones, extremal rays, and the A-Conjecture.

• YouTube
• 53 minutes
• Self-Paced
• Conference Talk

Low Dimensional Topology and Circle-valued Morse Functions

1 rating

Explore taut foliations in 3-manifolds with Heegaard genus two, examining the connection between left-orderable fundamental groups and co-orientable taut foliations in closed, orientable, irreducible 3-manifolds.

• YouTube
• 1 hour
• Self-Paced
• Conference Talk

The $K(\pi, 1)$ Conjecture - Part 2

1 rating

Explore the recent proof of the classical K(π,1) conjecture for affine Artin groups, delving into its mathematical intricacies and implications for algebraic topology.

• YouTube
• 56 minutes
• Self-Paced
• Free Video

Equivariant Birational Geometry of 3-Dimensional Projective Space

1 rating

Explore G-equivariant birational geometry of 3D projective space, focusing on finite group actions and their impact on fibrations into rational curves or surfaces.

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

G-Equivariant Hodge Atoms

Explore G-equivariant Hodge atoms and their applications in singularity theory, including Chen-Ruan cohomology enhancements and potential birational classification systems.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

Topological Toric Mirror Monodromies

Explore mirror symmetry actions on toric varieties through Legendrian moduli spaces, connecting algebraic geometry with braid group theory in singularity analysis.

• YouTube
• 52 minutes
• Self-Paced
• Free Video

Deformations and Mutations of Affine Gorenstein Toric Varieties

Explore the correspondence between one-parameter deformations of affine Gorenstein toric varieties and mutations of Laurent polynomials with Newton polytopes.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Lagrangian Fibrations on Calabi-Yau Hypersurfaces II

Explore advanced combinatorics and integral affine structures in Lagrangian torus fibrations on Calabi-Yau toric hypersurfaces with discriminant analysis.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

Hodge Atoms - Definition, Invariants, and Applications

Explore Hodge atoms, their fundamental invariants, and practical applications in singularity theory through advanced mathematical analysis.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Lagrangian Fibrations on Calabi-Yau Hypersurfaces I

Explore Lagrangian torus fibrations on Calabi-Yau hypersurfaces using ironing coefficients and convex potentials to break manifolds into local models.

• YouTube
• 53 minutes
• Self-Paced
• Free Video

Refined Donaldson-Thomas Invariants and Milnor Fibres

Explore quadratic A^1-versions of Donaldson-Thomas invariants and their connections to Milnor fibres, Euler characteristics, and Behrend functions in singularity theory.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

The Logarithmic Smoothness of Non-d-Semistable Normal Crossing Schemes

Explore advanced logarithmic geometry through sharp lax log structures on normal crossing schemes, extending beyond d-semistable cases with infinitesimal lifting properties.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

F-bundles and A-model F-bundles for Hodge Atoms

Explore F-bundles and their role in defining A-model F-bundles essential for understanding Hodge atoms in singularity theory.

• YouTube
• 52 minutes
• Self-Paced
• Free Video

Mutations and Deformations of Gorenstein Toric Varieties via Log Resolutions

Explore mutations and deformations of Gorenstein toric varieties through logarithmic geometry, connecting mirror symmetry concepts with new mathematical approaches.

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