Heegaard Floer Homology Courses and Certifications

ICTP Mathematics

Frontiers in Geometry and Topology Summer School

Explore advanced topics in geometry and topology including Heegaard Floer homology, Dirac operators, pseudoholomorphic curves, and Seiberg-Witten equations through expert lectures.

• YouTube
• 15 hours 34 minutes
• Self-Paced
• Free Video

Centre International de Rencontres Mathématiques

Moduli Spaces in Symplectic Topology and Gauge Theory

Explore advanced symplectic topology and gauge theory through moduli spaces, covering Floer theory, holomorphic curves, and contact homology with leading experts.

• YouTube
• 8 hours 41 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

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

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

Symplectic Rigidity of Anosov Flows Under Orbit Equivalence

Explore how orbit equivalent Anosov flows preserve symplectic invariants through Liouville structures, revealing deep connections between dynamics and symplectic geometry.

• 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

University of Chicago Department of Mathematics

Symplectic Manifolds and Derived Orbifolds - Lecture 3

Explore symplectic manifolds and derived orbifolds in this advanced geometry lecture, examining 40 years of developments since Floer's groundbreaking work in symplectic topology.

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

University of Chicago Department of Mathematics

Symplectic Manifolds and Bordism - Lecture 2

Explore symplectic manifolds and bordism in this advanced topology lecture, building on Gromov-Floer theory to understand modern developments combining homotopy theory with Morse theory.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

University of Chicago Department of Mathematics

Cotangent Bundles and the Hopf Map - Symplectic Topology 40 Years After Floer - Lecture 1

Explore symplectic topology's evolution from Poincaré to modern homotopy theory methods, focusing on cotangent bundles, Hopf maps, and Lagrangian submanifolds.

• YouTube
• 1 hour 9 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

Fields Institute

Introduction to Wrapped Fukaya Categories - Part 1

Dive into wrapped Fukaya categories with foundational concepts and mathematical structures in this advanced geometry lecture from the University of Toronto.

• YouTube
• 2 hours 5 minutes
• Self-Paced
• Free Video

Institute for Advanced Study

Hecke Algebras Via Morse Theory of Loop Spaces

Explore advanced symplectic geometry through Morse theory applications to loop spaces and higher-dimensional Heegaard Floer homology computations.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Fields Institute

Introduction to Wrapped Fukaya Categories - Part 2

Delve into advanced concepts of wrapped Fukaya categories in this comprehensive mathematical exploration by Benjamin Gammage from the University of Toronto.

• YouTube
• 1 hour 58 minutes
• Self-Paced
• Free Video