IMSA Courses

Subtly Knotted Surfaces Separated by Many Internal Stabilizations

Exploration of smoothly knotted surfaces in 4-manifolds, focusing on isotopy, internal stabilizations, and diffeomorphisms. Discusses infinite collections of surfaces with unique properties and infinite stabilization diameter.

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

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

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

Instantons, Suspension, and Surgery

Explore advanced concepts in gauge theory, including instantons, suspension, and surgery techniques for manifolds with boundary components and their applications in cobordism maps.

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

Instantons, Suspension, and Surgery - Part 1

Explore Dehn surgery number in 3-manifolds, using mod 2 instanton homology and Froyshov's q_3 invariant to prove existence of integer homology 3-spheres with arbitrarily large surgery numbers.

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

Fan Ye, Harvard University - 2-Torsions in Singular Instanton Homology

Exploration of 2-torsions in singular instanton homology for knots, comparing complex and Z/2 coefficients, with focus on fibered knots and genus 1 knot surgeries.

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

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

Toda Lattice, Billiards & the Viterbo Conjecture

Exploração da relação entre o reticulado de Toda, bilhares e a conjectura de Viterbo, com foco em sistemas integráveis e transformações simpléticas de produtos lagrangianos.

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

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

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

Fillable Contact Structures From Positive Surgery

Exploring conditions for fillable contact structures from positive surgery on Legendrian knots, with applications to topological consequences and lens space surgeries.

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

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

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

PL-Surfaces in Homology 4-Balls

Exploration of PL-surfaces in homology 4-balls, discussing minimum genus of PL surfaces and their bounds in homology balls using Heegaard Floer homology. Joint research findings presented.

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

Equivariant Rokhlin, Eta, and Kappa Invariants of Seifert-Fibered Homology Spheres

Explore equivariant Rokhlin, eta, and kappa invariants of Seifert-fibered homology spheres in this advanced topology talk, delving into gauge theory applications and low-dimensional manifold properties.

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