IMSA Courses

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

Homological Mirror Symmetry - Lagrangian SYZ Fibrations

Explore Lagrangian SYZ fibrations in symplectic geometry, focusing on integral affine manifolds with singularities and the construction of local models and gluing techniques.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Homological Mirror Symmetry - Toward the Logarithmic Hilbert Scheme

Explore logarithmic geometry and its applications in mirror symmetry, focusing on the development of a logarithmic Hilbert scheme and its implications for degenerations and tropical mathematics.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Homological Mirror Symmetry - Atsushi Takahashi, Osaka University

Exploring generalized root systems of type D, constructing Frobenius manifolds, and examining their potential applications in algebraic geometry and mathematical physics.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Homological Mirror Symmetry - Nikita Nekrasov

Explore homological mirror symmetry and integrable systems through Lax operators, intersection theory, and gauge theory. Delve into Garnier models, Hitchin systems, and quiver gauge theories.

• YouTube
• 56 minutes
• On-Demand
• Free Video

Homological Mirror Symmetry - Moduli Space of Non-Archimedean Holomorphic Disks Pt. II

Explore non-Archimedean holomorphic disks in affine log Calabi-Yau varieties, covering boundary conditions, smoothness, dimension, and properness. Gain insights into non-Archimedean mirror symmetry and related theories.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Homological Mirror Symmetry - Categorical Donaldson-Thomas Theory of C^3 and Beyond

Explore advanced concepts in Donaldson-Thomas theory, including categorifications, refinements, and applications to C^3 and beyond, with a focus on categorical invariants and correspondences.

• YouTube
• 1 hour
• On-Demand
• Free Video