Knot Algebras, Hopf Algebras, Quantum Algebras

Quantum Invariants of Knots and Links

Vassiliev Invariants

TQFT, Topological Quantum Computing

Link Homology and Categorification

Quandles and Quandle Cohomology

Knots and Links in 3- and 4-Manifolds

Invariants of 3- and 4-Manifolds

Skein Modules

Braids

Orderability of Braid Groups, 3-Manifold Groups and Knot Groups

Virtual Knot Theory

Hyperbolic Knots and Geometric Structures on 3-Manifolds

Physical Knots, Topology of Fluid Flows, Surgery

Applications to Natural Sciences (Physics, Biology, Chemistry, …)