Heegaard Floer Homology Courses and Certifications

Institute for Advanced Study

Floer Cohomology and Arc Spaces - Mark McLean

Explore Floer cohomology, arc spaces, and symplectic geometry with Mark McLean. Delve into contact structures, jet spaces, and mapping moduli spaces in this advanced mathematical lecture.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Introduction to Fukaya Categories - James Pascaleff

Explore symplectic geometry fundamentals for Fukaya categories, covering symplectic manifolds, Lagrangian submanifolds, exactness conditions, and more in this comprehensive lecture.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

IMSA

Introductory Lectures on Singularities and Mirror Symmetry - Part 2

Explore advanced mathematical concepts in mirror symmetry, including disk potential, Jacobian rings, matrix factorization, and quantum cohomology through theoretical frameworks.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

Institute for Advanced Study

Plumber's Algebra Structure on Symplectic Cohomology

Delve into advanced symplectic geometry concepts, exploring Plumber's PROP structures, nodal Riemann surfaces, and their applications to cohomological field theories and curve counting methods.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Institute for Advanced Study

Bounding Lagrangian Intersections Using Floer Homotopy Theory

Delve into advanced mathematical concepts exploring Lagrangian intersections through Floer homotopy theory, featuring new lower bound calculations and Steenrod squares applications in symplectic geometry.

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

Institut des Hautes Etudes Scientifiques (IHES)

Complete Riemannian 4-Manifolds with Uniformly Positive Scalar Curvature Metric

Explore the relationship between geometry and topology in 4-manifolds, focusing on conditions for contractible 4-manifolds to admit uniform positive scalar curvature metrics and the resulting topological insights.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

IMSA

Curious Filtration from the Floer Theory and C*-Actions

Explore the construction of symplectic cohomology for open symplectic manifolds with pseudo-holomorphic C*-actions, including filtration applications for ADE resolutions and Higgs bundles.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Institute for Advanced Study

A Local Quasimorphism Property for Link Spectral Invariants

Delve into the mathematical exploration of link spectral invariants on symplectic surfaces, focusing on their local quasimorphism properties for Lagrangian circles under specific area constraints.

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

Institute for Advanced Study

Equivariant Floer Theory for Symplectic C*-manifolds

Delve into equivariant Floer theory for symplectic C*-manifolds, exploring recent progress on non-compact symplectic manifolds with Hamiltonian circle actions and the resulting filtrations on quantum cohomology.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Institute for Advanced Study

Continuation Maps for the Morse Fundamental Group

Explore continuation maps for Morse fundamental groups and their functoriality properties in symplectic topology through combinatorial recovery of fundamental groups from Morse-Smale pairs.

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

Institute for Advanced Study

Equivariant Lagrangian Non-Displacements

Explore ℤ2-equivariant Floer cohomology to detect non-displaceability of Lagrangian submanifolds under group actions, focusing on S¹-invariant Lagrangians in ℂⁿ using Floer-Euler classes.

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

Institute for Advanced Study

From Symplectic Weyl Laws to Homeomorphism Groups and Beyond

Explore how Floer theory and symplectic topology reveal the non-simplicity of area-preserving homeomorphism groups, extending classical invariants to continuous settings.

• YouTube
• 1 hour 13 minutes
• Self-Paced
• Free Video

Stony Brook Mathematics

100 Years of Morse Theory

Explore the evolution of Morse theory from its 1925 origins to modern applications in symplectic topology, covering Witten's formalism and Floer's developments.

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

BIMSA

Lattice Homology - The Unifying Construction

Explore lattice homology as a unifying mathematical construction in this advanced topology lecture by András Némethi at BIMSA's international conference.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

BIMSA

Topological 5D N=2 Gauge Theories - Mirror Symmetry and Langlands Duality of A-infinity Categories of Floer Homologies

Explore advanced connections between 5-dimensional supersymmetric gauge theories, mirror symmetry, and Langlands duality through A-infinity categories of Floer homologies.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video