Anosov Flows on 3-Manifolds
Dive into Anosov flows on 3-manifolds, exploring their chaotic yet stable nature, classification challenges, and recent advancements in low-dimensional geometric topology.
Low-Dimensional Solenoidal Manifolds
Exploración de manifolds solenoidales de baja dimensión, sus propiedades topológicas y estructurales, y nuevos resultados en este campo de la geometría y topología.
Algebraization of Low-Dimensional Topology - Lecture 4
Explore algebraic presentations of cobordism categories in 3 and 4 dimensions, focusing on torus-based structures and their implications for Topological Quantum Field Theories.
Using Machine Learning to Formulate Mathematical Conjectures - IPAM at UCLA
Explore how machine learning aids mathematicians in formulating conjectures, focusing on a discovery linking low-dimensional topology and geometry, with insights on the method's potential and limitations.
Square Pegs and Round Holes
Introduction to lattice homology: algebraic structure for studying three-manifolds. Explores integer lattice approximations of ellipsoids, with implications for navigating institutions not designed for one's needs.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Measure and Smooth Rigidity of Lattice Actions in Low Dimensions - Federico Rodriguez-Hertz
Explore measure and smooth rigidity of lattice actions in low dimensions with Federico Rodriguez-Hertz, delving into advanced mathematical concepts and their applications.