IMSA Courses

Logarithmic Transformations and Vector Bundles on Elliptic Surfaces via O-Minimal Geometry II

Explore logarithmic transformations and vector bundles on elliptic surfaces through o-minimal geometry, examining their impact and applications in various mathematical fields.

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

Logarithmic Transformations and Vector Bundles on Elliptic Surfaces via O-Minimal Geometry I

Explore logarithmic transformations and vector bundles on elliptic surfaces through o-minimal geometry, examining their impact and applications in various mathematical fields.

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

Quantum Toric Geometry and Tame Geometry via Motivic Rings II

Explore the connection between quantum toric manifolds and tame geometry through Hodge number computations of LVM manifolds, providing insights for future research in non-commutative geometry.

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

Quantum Toric Geometry and Tame Geometry via Motivic Rings I

Explore the connection between quantum toric manifolds and tame geometry through Hodge number computations of LVM manifolds, providing insights for future research in non-commutative geometry.

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

Generalized Complex Branes, Doubling, and Shifted Symplectic Geometry, Part I

Explore symplectic approaches to generalized complex geometry, focusing on brane construction and implications for Kaehler geometry. Delve into shifted symplectic geometry and homotopy complex structures.

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

Generalized Complex Branes, Doubling, and Shifted Symplectic Geometry, Pt II

Explore symplectic approaches to generalized complex geometry, focusing on brane construction and implications for generalized Kaehler geometry. Delve into shifted symplectic geometry and homotopy complex structures.

• YouTube
• 1 hour
• 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