IMSA Courses

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

Perverse Sheaves on Varieties with Large Fundamental Group

Explore perverse sheaves on Kähler manifolds, focusing on a generalization of the Singer-Hopf conjecture and its proof using Shafarevich conjecture ideas. Joint work with Donu Arapura presented.

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

Hecke Actions on Loops and Periods of Iterated Shimura Integrals

Exploration of Hecke actions on loops and periods of iterated Shimura integrals, focusing on SL_2(Z) and modular curves, with insights into mixed modular motives and Galois action.

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

Mixed Hodge Structures on Cohomology Jump Ideals

Explore mixed Hodge structures on cohomology jump ideals in representation varieties, extending Goldman and Millson's work to non-compact Kähler manifolds and variations of mixed Hodge structures.

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

Complex Hyperbolicity and Representations of the Fundamental Group in Non-Compact Varieties

Explore complex hyperbolicity and fundamental group representations in quasi-projective varieties, blending archimedean and non-archimedean approaches to extend previous research in algebraic geometry.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video