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

International Mathematical Union

Jacob Rasmussen - Floer Homology of 3-Manifolds with Torus Boundary

Explore advanced concepts in Floer homology, focusing on 3-manifolds with torus boundary. Gain insights into cutting-edge mathematical research and its applications in topology.

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

Institute for Advanced Study

Floer Homology with DG Coefficients - Applications to Cotangent Bundles

Explore Floer homology with DG coefficients and its applications to cotangent bundles. Gain insights into symplectic geometry and dynamical systems through advanced mathematical concepts.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

NCCR SwissMAP

Bordered-Sutured Floer Homology as a Sutured TQFT

Explore advanced quantum topology concepts through bordered-sutured Floer homology and its applications as a sutured TQFT in this in-depth lecture by J. Rasmussen.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Integral Floer Homology Theory

Delve into Hamiltonian Floer theory over integers for compact symplectic manifolds, exploring FOP transversality, flow categories, and applications to non-contractible periodic orbits and geometric uniruledness.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

ICTP Mathematics

Monopole Floer Homology and Invariant Theta-Characteristics

Explore advanced concepts in geometry and topology, focusing on monopole Floer homology and invariant theta-characteristics in this Princeton University lecture.

• YouTube
• 48 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

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

IMSA

Rational Slice Genus Bounds from Knot Floer Homology

Exploring rational slice genus of knots using relative adjunction inequalities and knot Floer homology, with applications to Floer simple knots and insights from 4-dimensional topology.

• YouTube
• 1 hour
• 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

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

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

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