. The most relevant quantities of the solution, such as its energy, can be expressed through certain holomorphic integrals on the curve. This allows for a classification of finite gap solutions analogous to the general solution of strings in flat space. The role of fermions in the context of the algebraic

Vertex operators appeared in the early days of string theory as local operators describing propagation of string states. Mathematical analogues of these operators were discovered in representation theory of affine Kac-Moody algebras in the works of Lepowsky–Wilson [LW] and I. Frenkel–Kac [FK

with certain properties lead to commuting differential operators reconfirming forgotten work by Burchnell and Chaundy [6]. Inspired by Krichever's ideas, Mumford [24] establishes then a dictionary between commutative rings of (differential and difference) operators and algebraic curves using purely

Abstract. We show that if a pair of meromorphic functions parametrize an algebraic curve then they have a common right factor, and we use this to derive a variety of results on algebraic curves. 1.

Abstract. We survey a recent application of algebraic curves over finite fields to the constructions of authentication codes. 1.

Abstract. An effective description of the join of algebraic curves in the complex projective space P n is given. 1

Abstract. The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be approached from a computational viewpoint. 1.

Abstract. Algebraic curves over finite fields are being extensively used in the design of public-key cryptographic schemes. This paper surveys some topics in algebraic curve cryptography, with an emphasis on recent developments in algorithms for the elliptic and hyperelliptic curve discrete

We develop methods for the variational design of algebraic curves. Our approach is based on truly geometric fairness criteria, such as the elastic bending energy. In addition, we take certain feasibility criteria for the algebraic curve segment into account. We describe a computational technique

Abstract. For any algebraic curve C and n ≥ 1, P. Etingof introduced a ‘global ’ Cherednik algebra as a natural deformation of the cross product D(C n)⋊Sn, of the algebra of differential operators on C n and the symmetric group. We provide a construction of the global Cherednik algebra in terms