IMSA Courses

Low Dimensional Topology and Circle-Valued Morse Functions

Exploración de límites en el número de asas de variedades suturadas, utilizando argumentos geométricos y desarrollando una función de número de asas en homología de segundo grado.

• YouTube
• 55 minutes
• On-Demand
• Conference Talk

Low Dimensional Topology - Flipping Heegaard Splittings

Explore Heegaard splittings in topology, focusing on oriented isotopy of splitting surfaces and the possibility of "flipping" sides. Examine contexts, examples, and implications in this advanced mathematical discussion.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Conference Talk

Low Dimensional Topology and Circle-valued Morse Functions

Explore applications of guts in 3-manifolds, including minimal volumes of hyperbolic manifolds and Euler characteristic control in Dehn fillings. Gain insights into advanced topological concepts and their implications.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Conference Talk

Low Dimensional Topology and Circle-Valued Morse Functions

Explore knot complements, Seifert surfaces, and sutured manifolds in low-dimensional topology. Discover unique decompositions and their implications for the Kakimizu complex and Thurston norm.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Conference Talk

Low Dimensional Topology and Circle-valued Morse Functions

Explore annular links, double branched covers, and annular Khovanov homology. Discover how these concepts relate to braid closures and the wrapping conjecture in low-dimensional topology.

• YouTube
• 57 minutes
• On-Demand
• Conference Talk

Low Dimensional Topology and Circle-valued Morse Functions

Explore forbidden minor multibranched surfaces and critical complexes in 3-sphere embeddings. Analyze K5 × S1 and K3,3 × S1 families, critical complexes, and their properties in low-dimensional topology.

• YouTube
• 59 minutes
• On-Demand
• Conference Talk

Low Dimensional Topology and Circle-valued Morse Functions

Explores non almost-fibered knots in 3-sphere, analyzing circular thin positions and Seifert surfaces. Focuses on hyperbolic genus one knots with multiple disjoint Seifert surfaces, demonstrating their complex circular thin positions.

• YouTube
• 51 minutes
• On-Demand
• Conference Talk

Low Dimensional Topology and Circle-valued Morse Functions

Explore instanton Floer homology's surgery formula, its applications in computing 3-manifold invariants, and connections to SU(2)-representations of fundamental groups.

• YouTube
• 58 minutes
• On-Demand
• Conference Talk

Low Dimensional Topology and Circle-valued Morse Functions

Explore singular fibrations in knot exteriors and their extensions over handlebodies, connecting handle-ribbon knots to circular Morse functions in low-dimensional topology.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Conference Talk

Orbifold Jet Differentials and Hyperbolicity Conjectures

Explore orbifold jet differentials and their role in hyperbolicity conjectures. Discuss limitations in extending classical results to orbifold contexts, based on collaborative research.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Kato-Usui Type Extension of General Period Map

Explore Kato-Usui theory for extending non-classical period maps, its applications, and potential future directions in algebraic geometry and Hodge theory.

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

Filtered Ends and Bochner Hartogs Dichotomy on Complete Kahler Manifolds

Explore filtered ends and Bochner Hartogs dichotomy on complete Kahler manifolds, examining relationships between generalized ends and first compactly supported cohomology.

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

Fake Projective Planes: Properties and Recent Progress

Explore fake projective planes: complex surfaces with unique properties, their construction via uniformization, and recent advancements in understanding their algebraic and geometric characteristics.

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

Exploring the Boundary of the Moduli Space of Stable Surfaces - I-Surfaces as a Test Case

Exploring I-surfaces: minimal complex surfaces with K^2=1 and p_g=2. Recent research on boundary points of KSBA compactification for I-surfaces' moduli space.

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

The Geometric Andre-Grothendieck Period Conjecture

Explore complex algebraic varieties, period integrals, and the Ax-Schanuel conjecture. Delve into transcendence theory of period maps and the Andre-Grothendieck period conjecture's functional version.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video