Mathematicians survey new applications of

algebraic curves that the recent development of computational techniques and significant growth in computer power have made possible.

Grau, "Coexistence of limit cycles and invariant

algebraic curves for a Kukles system," Nonlinear Analysis.

Meilhan, A linking invariant for

algebraic curves, arXiv:1602.04916.

As an intermediate step towards the third result, we also show that for a fixed family of plane

algebraic curves with s degrees of freedom, every set of n points in the plane has a subset of [OMEGA]([n.sup.1-1/s]) points incident to a single curve, or a subset of [OMEGA]([n.sup.1/s]) points such that at most s of them lie on a curve.

Hilbert's 16th problem has two parts and its first part is on the topology of

algebraic curves and surfaces.

Rationality of the offsets to

algebraic curves and surfaces.

Algebraic curves are a classic research object in mathematics.

One particularly nice way of studying general parametric cubics can be found in [3] which treats them as general

algebraic curves, determines their properties, and then specializes the results to the family of general parametric cubics.

Other topics include counting

algebraic curves with tropical geometry, block triangular bilinear forms and braid group action, the topicalization method in cluster algebras, and an application of the max-plus spectral theory to an ultradiscrete analogue of the Lax pair.

HARIS, Real

algebraic curves, Annales scientifiques de l'ENS, 4 eme sErie, tome 14, no.