3-Manifold Groups and Fundamental Group Conjectures - Part II
Explorez les conditions conjecturales impliquant qu'un groupe est le groupe fondamental d'une 3-variété compacte, en examinant les conjectures de Cannon et Wall et leurs interconnexions.
Virtually Free-by-Cyclic Groups
Explore recognition methods for virtually free-by-cyclic groups within hyperbolic compact special groups using homology techniques.
Subgroup Separability of 3-Manifold Groups and Its Applications
Explore subgroup separability in 3-manifold groups, its characterization via torus decomposition, and applications to subgroup distortion and Grothendieck rigidity. Joint work with Hoang Thanh Nguye.
Division, Group Rings, and Negative Curvature in Low-Dimensional Topology
Explore low-dimensional topology through group rings and division algorithms, focusing on 2-complexes and hyperbolic manifolds. Gain insights into fundamental group structures and cell-decomposition complexity.
Geometrization and its Consequences in 3-Manifold Topology - Lecture 3
Explore Thurston's geometric perspective on 3-manifolds, Perelman's Geometrization Theorem, and their impact on topology, algorithms, and group theory in 3D geometry.
Profinite Rigidity, Triangle Groups, and Seifert Fibred Spaces
Explore profinite rigidity in 3-manifold groups, examining unique determination by finite images and distinctions between finitely presented and generated groups.
An Approach to Simon's Conjecture
Explore fundamental group epimorphisms between 3-manifolds and their implications for knot genera. Investigate conjectures related to Simon's conjecture in knot theory.
CAT(0) Cube Complexes - Lecture 1
Explore CAT(0) cube complexes in this introductory minicourse, delving into fundamental concepts and applications in geometric group theory.
3-Manifold Groups and Fundamental Group Conjectures - Lecture 3
Explorez les conditions conjecturales impliquant qu'un groupe est le groupe fondamental d'une 3-variété compacte, en examinant les conjectures de Cannon et Wall ainsi que leurs interconnexions.
Minimal Surfaces and the Allen-Cahn Equation on 3-Manifolds
Explore minimal surfaces and the Allen–Cahn equation on 3-manifolds, focusing on recent results and the multiplicity-one theorem in three dimensions.
Analytic and Reidemeister Torsions of Digraphs and Path Complexes
Explore Reidemeister and analytic torsions on finite digraphs using path homology theory. Learn about Hodge Laplace operators, torsion identities, and formulas for Cartesian products and joins.
Symplectomorphism Invariants of Open Domains
Explore symplectomorphism invariants of open domains, focusing on zeta functions, Reeb dynamics, and equivariant symplectic homology to distinguish toric domains.
Pseudo-Isotopy and Diffeomorphisms of 4-Manifolds
Explore recent advancements in pseudo-isotopy theory and its applications to studying diffeomorphisms of 4-manifolds with David Gabai.
Derived Approach to Highest Weight Categories
Explore highest weight categories in Representation Theory, examining their interpretation through exact categories, abelian envelops, and exceptional collections in derived categories.
Topology and Artificial Intelligence - Applications and Recent Progress
Explore recent advancements in algebraic topology and AI, including language models for homotopy groups and statistical modeling for complex networks and diseases.
Curvature-Homogeneous Riemannian 3-Manifolds and Integrable Systems
Explore curvature-homogeneous Riemannian 3-manifolds, surveying known examples and recent discoveries. Delve into connections with integrable systems, particularly Toda lattices, to construct new explicit examples.
Knot Invariants from Finite Dimensional Integration
Explore finite dimensional integration for computing powerful knot invariants, surpassing traditional methods in efficiency and rigor while challenging established notions in knot theory.
Symplectic Topology, Stability Conditions and Quadratic Differentials
Explore connections between symplectic topology, stability conditions, and quadratic differentials in Fukaya categories and mapping class groups.
Symplectic Topology, Stability Conditions and Quadratic Differentials
Explore connections between symplectic topology, stability conditions, and quadratic differentials in Fukaya categories and mapping class groups.
Tightness and Legendrian Surgery in Contact Structures
Explore contact structures, open book decompositions, and tightness characterization in 3-manifolds. Investigate preservation of tightness under Legendrian surgery.
Ricci Limit Spaces are Semi-Locally Simply Connected
Explore Ricci limit spaces and their semi-local simple connectivity, delving into fundamental groups and Gromov-Hausdorff convergence of Riemannian manifolds.