Heegaard Floer Homology Courses and Certifications

IAS | PCMI Park City Mathematics Institute

Heegaard Floer Homology

Dive into Heegaard Floer homology through comprehensive lectures covering fundamental concepts and advanced applications in low-dimensional topology and knot theory.

• YouTube
• 3 hours 53 minutes
• On-Demand
• Free Video

Simons Foundation

Real Heegaard Floer Homology - March 27, 2025

Delve into the construction of real Heegaard Floer homology for 3-manifolds with involution, exploring its topological invariance, connections to Miyazawa's work, and applications to exotic RP^2-knots.

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

Institute for Advanced Study

Khovanov and Heegaard Floer Homology

Explore advanced connections between Khovanov and Heegaard Floer homology in this specialized symplectic geometry seminar from Princeton University and IAS.

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

International Mathematical Union

Jennifer Hom: Homology Cobordism and Heegaard Floer Homology

Explore homology cobordism and Heegaard Floer homology, delving into manifolds, theorems, and chain complexes in this advanced mathematical lecture.

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

ICTP Mathematics

Heegaard Floer Homology and Topology in Dimensions 3.5 - 3

Explore Heegaard Floer homology and its applications in low-dimensional topology, focusing on dimensions between 3 and 3.5 in this advanced mathematical lecture.

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

ICTP Mathematics

Heegaard Floer Homology and Topology in Dimensions 3.5 - 2

Explore Heegaard Floer homology and its applications in low-dimensional topology, focusing on dimensions between 2 and 3.5 with expert Jen HOM.

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

ICTP Mathematics

Heegaard Floer Homology and Topology in Dimensions 3.5 - 1

Explore Heegaard Floer homology and its applications in low-dimensional topology, focusing on dimensions 3.5 to 1 in this advanced mathematics lecture.

• YouTube
• 1 hour 35 minutes
• On-Demand
• Free Video

Banach Center

Detecting Corks Using Heegaard Floer Homology

Explore Heegaard Floer homology's role in detecting corks and discover new examples addressing Gompf's question in 4-manifold exotic smooth structures.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

QuantumTopology

Ph. Kirablev - Combinatorial Description of Heegaard Floer Homology

Explore combinatorial approaches to Heegaard Floer homology, a powerful invariant in low-dimensional topology, with insights from Ph. Kirablev's lecture on advanced mathematical techniques.

• YouTube
• 1 hour 24 minutes
• On-Demand
• Free Video

University of Chicago Department of Mathematics

Heegaard Floer Homology: From Heegaard Diagrams to Holomorphic Disks - Lecture 2

Delve into Heegaard Floer homology, a tool for studying three- and four-dimensional manifolds using symplectic geometry-inspired methods, including applications and computational advances.

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

IMSA

Instanton Floer Homology and Heegaard Diagrams

Exploring the connection between instanton Floer homology and Heegaard diagrams in 3-manifolds, with insights on extracting information and potential applications in topology.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

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
• On-Demand
• Free Video

Western Hemisphere Virtual Symplectic Seminar

Composition, DG-Modules, and Cobordism Maps in Bordered Floer Homology

Explore bordered Floer homology, dg-modules, and the topological interpretation of module homomorphism composition in Heegaard Floer complexes. Gain insights into cobordism maps and their consequences.

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

Western Hemisphere Virtual Symplectic Seminar

Coherent Orientations of DGA Maps Associated to Exact Lagrangian Cobordisms

Explore coherent orientations of DGA maps in exact Lagrangian cobordisms, focusing on combinatorial formulas for mini-dipped pinch moves and applications to Heegaard Floer Homology.

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

Banach Center

Bordered Floer Theory, Hochschild Homology, and Links in S^1 × S^2

Explore spectral sequences linking Khovanov homology to Heegaard Floer homology and their analogues for links in S^1×S^2, involving bordered Floer theory and Hochschild homology.

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