IMSA Courses

Low Dimensional Topology and Circle-valued Morse Functions

1 rating

Explore taut foliations in 3-manifolds with Heegaard genus two, examining the connection between left-orderable fundamental groups and co-orientable taut foliations in closed, orientable, irreducible 3-manifolds.

• YouTube
• 1 hour
• Self-Paced
• Conference Talk

The $K(\pi, 1)$ Conjecture - Part 2

1 rating

Explore the recent proof of the classical K(π,1) conjecture for affine Artin groups, delving into its mathematical intricacies and implications for algebraic topology.

• YouTube
• 56 minutes
• Self-Paced
• Free Video

Interpolation for Polynomials in Two Variables

1 rating

Explore advanced polynomial interpolation techniques in two variables, covering dimension counts, Picard groups, and conjectures like Segre's and Nagata's. Delve into cones, extremal rays, and the A-Conjecture.

• YouTube
• 53 minutes
• Self-Paced
• Conference Talk

Coinduction for Comodule Algebras

1 rating

Explore coinduction for comodule algebras, focusing on constructing C_c(G)-comodule algebras from C(H)-comodule algebras for finite H, and its implications for crossed products and group cases.

• YouTube
• 44 minutes
• Self-Paced
• Free Video

Equivariant Birational Geometry of 3-Dimensional Projective Space

1 rating

Explore G-equivariant birational geometry of 3D projective space, focusing on finite group actions and their impact on fibrations into rational curves or surfaces.

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

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video