IMSA Courses

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

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

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

Skein Exact Triangles in Equivariant Singular Instanton Theory

Explore knot signatures and singular instanton homology, focusing on skein exact triangles in equivariant theory. Uncover new insights into link invariants and their categorifications.

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

Low Dimensional Topology and Circle-valued Morse Functions

Explore Khovanov homology of torus braids, characterizing simplified complexes and their applications in quantum topology. Gain insights into recent advancements and conjectures in low-dimensional topology.

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

Low Dimensional Topology and Circle-Valued Morse Functions

Explore the Kakimizu complex for genus one hyperbolic knots, examining its structure, dimensions, and examples across various dimensions in 3-sphere topology.

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

Hodge Theory of Abelian Covers of Algebraic Varieties

Explore Hodge Theory of Abelian Covers in algebraic varieties, covering Alexander modules, multivariables, and transformations. Gain insights into advanced mathematical concepts and their applications.

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

Curvature Formula for Direct Images of Relative Canonical Bundles with Poincaré Type Twist

Curvature formula for direct images of relative canonical bundles with Poincaré type twist, improving positivity results and potentially proving Kobayashi hyperbolicity of moduli spaces.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Periods, Shafarevich Maps and Applications in Algebraic Geometry

Explore periods, Shafarevich maps, and their applications in mathematics, covering key concepts, historical context, and advanced theoretical proofs.

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

Quadratic Forms in Surface Automorphisms and Singularity Theory

Explore pseudo-periodic surface automorphisms, quadratic forms, and their applications in singularity theory. Gain insights into Milnor fibers and monodromy automorphisms.

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

Rigid Compact Complex Manifolds - Properties and Examples

Explore rigid compact complex manifolds, their properties, and recent findings in product-quotient varieties, addressing long-standing questions in algebraic geometry.

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

The Miyaoka-Yau Equality for Pairs

Explore Miyaoka-Yau Equality for klt pairs, characterizing ball quotients through Chern classes. Gain insights into this advanced mathematical concept and its applications.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

A Homological Interpretation of Higher Du Bois and Higher Rational Singularities

Explore homological interpretations of higher Du Bois and rational singularities, focusing on hypersurfaces and characteristic classes. Gain insights into advanced algebraic geometry concepts.

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