Low-Dimensional Topology Courses and Certifications

ICTP Mathematics

Lattices in Low-Dimensional Topology

Explore advanced concepts in low-dimensional topology, focusing on lattice structures and their applications in geometric and topological analysis.

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

IMSA

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

IMSA

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

IMSA

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

IMSA

Hilbert Schemes of Plane Curve Singularities and Matrix Factorizations

Explore connections between algebraic geometry and topology through plane curve singularities, Hilbert schemes, and matrix factorizations in this advanced mathematics lecture.

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

IMSA

Homology Cobordism and the Geometry of Hyperbolic Three-Manifolds

Explore the interaction between hyperbolic geometry and homology cobordism using monopole Floer homology, focusing on subgroups generated by hyperbolic homology spheres.

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

IMSA

Ribbon Concordances and Slice Obstructions: Experiments and Examples

Explore ribbon concordances between knots, computational methods, and results in low-dimensional topology. Joint work with Nathan Dunfield on slice obstructions and experimental approaches.

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

IMSA

Gauge Theory and Low Dimensional Topology - Conference Lecture

Explore gauge theory and low-dimensional topology with expert insights from Paul Feehan in this engaging 48-minute conference talk at the University of Miami.

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

IMSA

Smooth Closing Lemma for Area-Preserving Diffeomorphisms of Surfaces

Explore the smooth closing lemma for area-preserving diffeomorphisms on surfaces, featuring a proof based on Weyl formula and Seiberg-Witten Floer homology. Joint work with Cristofaro-Gardiner and Prasad.

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

IMSA

Gauge Theory and Low Dimensional Topology

Explore gauge theory and low-dimensional topology with insights from MIT expert Tom Mrowka in this conference talk at the University of Miami.

• YouTube
• 1 hour 5 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

IMSA

An Exact Triangle in Monopole Floer Spectra

Explore an exact triangle for monopole Floer spectra, its application to almost-rational plumbings, and potential future calculations in this advanced topology conference talk.

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

IMSA

Characterizing Slopes for Alternating Knots

Exploration des pentes caractérisantes pour les nœuds alternés, examinant leur unicité lors de chirurgies rationnelles et discutant des progrès récents dans ce domaine de la topologie.

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

IMSA

Four-Genus Bounds from the 10/8+4 Theorem

Explore knot slicing obstructions and four-ball genus bounds using the 10/8+4 theorem. Learn about advanced techniques in gauge theory and low-dimensional topology.

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

IMSA

Low Dimensional Topology and Circle-Valued Morse Functions

Explore thin position theory for knots, links, and graphs, and its applications to width, tunnel number, and bridge number in topology. Learn about "cut"-incompressible surfaces and additivity of knot invariants.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Conference Talk