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
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
Rationality of the offsets to algebraic curves
are a classic research object in mathematics.
One particularly nice way of studying general parametric cubics can be found in  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.