Some applications of a model theoretic fact to (semi-) algebraic geometry

Algebraic algorithms and applications to geometry

Real algebraic numbers are the real numbers that are real roots of univariate polynomials with integer coefficients. We study exact algorithms, from a theoretical and an implementation point of view, that are based on integer arithmetic of arbitrary precision, for computations with real algebraic numbers and applications of these algorithms on problems and algorithms in non linear computational...

Semi-algebraic Geometry of Braid Groups

The braid group of n-strings is the group of homotopy types of movements of n distinct points in the 2-plane R. It was introduced by E. Artin [1] in 1926 in order to study knots in R. He gave a presentation of the braid group by generators and relations, which are, nowadays, called the Artin braid relations. Since then, not only in the study of knots, the braid groups appear in several contexts...

Some Questions in Algebraic Geometry

Frans Oort \Een zot kan meer vragen \One fool can ask more questions dan tien wijzen kunnen beantwoorden." than ten wise men can answer." Een oud Nederlands spreekwoord. An old Dutch saying. Introduction In June 1995 several mathematicians will gather in Utrecht for a conference on \Arithmetic and geometry of abelian varieties," and this seems a good occasion to share with them some of the ques...

Derandomizing Some Number-theoretic and Algebraic Algorithms

Some notions of D-algebraic geometry

When studying type-definable sets in closed Hasse fields, we observe a certain analogy with the case of algebraically closed fields. We show here in particular that connected type-definable groups can be described as “D-algebraic groups”, which is the natural equivalent for algebraic groups. However, many problems arise when we try to give a description of these geometric objects in the languag...