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.

Via the correspondence between

algebraic curves and floor diagrams [BM09, Theorem 2.

5) we first look for the branch of the

algebraic curve [[PSI].

The investigation of an

algebraic curve of the type exemplified in equation (1) has several potential uses:

For any irreducible plane

algebraic curve A [subset] [P.

Consider an

algebraic curve (a real surface) [summation] whose equation in [C.

van Kampen, On the fundamental group of an

algebraic curve, Amer.

Ten survey articles reflect invited lectures at the workshops

Algebraic Curves Over Finite Fields, held in November 2013, and Emerging Applications of Finite Fields, held in December 2013.

Rationality of the offsets to

algebraic curves and surfaces.

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.