Explores the transition of knots from practical applications to mathematical theory, covering equilibrium, tension analysis, ideal shapes, DNA mechanics, and pressure distributions.
Explores the dynamics of steady Euler flows on Riemannian manifolds, covering ideal fluids, Euler equations, Eulerisable flows, and obstructions to exhibiting plugs.
Introduces the quadratic linking degree in motivic knot theory, covering knot theory basics, oriented links, intersection theory, and examples like the Hopf and Solomon links.
Covers Smith theory in Floer persistence and dynamics, exploring classical mechanics invariants, Poincaré-Birkhoff theorem, and the Hofer-Zehnder conjecture.
Explores the design and synthesis of interlocked molecules like catenanes and rotaxanes, along with the structural and symbolic significance of knots and Borromean rings.
