IMSA Courses

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

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

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
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

Nearly Parallel G2-Structures on 7-Manifolds - Associative 3-Folds in Aloff-Wallach Spaces

Explore nearly parallel G2-structures on 7-manifolds, focusing on Aloff-Wallach spaces and Sasaki-Einstein manifolds. Learn about associative 3-folds and their construction in these spaces.

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

Coassociative Fibrations in G2 Geometry

Explore G2 geometry in 7D spaces, focusing on coassociative submanifolds. Learn about their properties, deformation theory, and constructions forming fibrations with singular fibers in 7-manifolds.

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