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.
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.
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.
The Thurston Norm of 3-Manifolds with a 2-Generator Fundamental Group
Explore the Thurston norm in 3-manifolds with 2-generator fundamental groups, delving into advanced concepts in quantum topology and geometric group theory.
Floer Theory and Quantum Groups
Explore Floer theory, quantum groups, and gauge theories in 3-manifolds. Discover connections between moduli spaces, Floer invariants, and skein modules in topological quantum field theory.
Low Dimensional Topology and Circle-Valued Morse Functions
Explore knot complements, Seifert surfaces, and sutured manifolds in low-dimensional topology. Discover unique decompositions and their implications for the Kakimizu complex and Thurston norm.
Gauge Fields and Categorification of Quantum Group Invariants of 3-Manifolds
Explore new link and 3-manifold invariants associated with Verma modules of U_q(sl_N), their properties, and potential categorification in 3-manifold homology.