We consider the class of curves of finite total curvature, as introduced by Milnor. This is a
natural class for variational problems and geometric knot theory, and since it includes both …

We investigate and solve the weak noise theory for the semidiscrete O'Connell-Yor directed
polymer. In the large deviation regime, the most probable evolution of the partition function …

Curvatures of Smooth and Discrete Surfaces Page 1 Discrete Differential Geometry, AI
Bobenko, P. Schröder, JM Sullivan and GM Ziegler, eds. Oberwolfach Seminars, Vol. 38 …

We study a simple model of bicycle motion: a segment of fixed length in multi-dimensional
Euclidean space, moving so that the velocity of the rear end is always aligned with the …

We express Darboux transformations of discrete polarised curves as parallel sections of
discrete connections in the quaternionic formalism. This immediately leads to the …

We propose a discrete surface theory in R3 that unites the most prevalent versions of
discrete special parametrizations. Our theory encapsulates a large class of discrete surfaces …

Modelling incompressible ideal fluids as a finite collection of vortex filaments is important in
physics (super-fluidity, models for the onset of turbulence) as well as for numerical …

In this paper, we consider the discrete deformation of the discrete space curves with
constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and …

We investigate the discrete-time motions of planar discrete curves, and derive discrete
integrable equations on a two-dimensional nonuniform lattice. In particular, we obtain the …

We construct explicit solutions to the discrete motion of discrete plane curves that has been
introduced by one of the authors recently. Explicit formulas in terms of the τ function are …