We use the Krammer representation of the braid group in Libgober’s invariant and construct a new multivariate polynomial invariant for curve complements: Krammer polynomial. We show that the Krammer polynomial of an essential braid is equal to zero. We also compute the Krammer polynomials of some certain n-gonal curves.

We show that we can break SIDH in (classical) polynomial time, even with a random starting curve $$E_0$$ .

In this paper, a new basis, to be called C-Bézier basis, is constructed for the space Γn = span{1, t, t2, . . . , tn−2, sin t, cos t} by an integral approach. Based on this basis, we define C-Bézier curves. We then show that such basis and curves share the same properties as the Bernstein basis and the Bézier curves in polynomial spaces respectively.  2003 Elsevier Science B.V. All rights rese...

We construct high rank solutions to Nahm's equations for boundary conditions that correspond the Dirac multimonopole. Here, spectral curve is explicitly known and we achieve integration by constructing a basis of polynomial tuples forms frame flow eigenline bundle over curve.

We give a method to generate polynomial approximations to constant mean curvature surfaces with prescribed boundary.