Colloquium Mathematics: Dr. R.P.Pannekoek

Title: Diophantus revisited

Abstract:

Historically, one of the first mathematicians to inquire about rational solutions to polynomial equations was Diophantus of Alexandria, who lived almost 2000 years ago. He has sometimes been described as the Father of Algebra, since his way of writing algebraic relations, sometimes called syncopated algebra, can be regarded as a major step on the way towards our  'modern' algebra. However, Diophantus' achievements are not limited to matters of notation. His methods for solving equations are equally impressive. I will discuss equations and solutions appearing in his main work, the "Arithmetica", and show that in solving them, Diophantus is effectively doing (what we would today call) birational geometry, i.e. the study of algebraic varieties up to birational equivalence. In particular, among the geometric objects encountered in his work are del Pezzo surfaces, K3 surfaces, and fibrations into conics and curves of genus 1. In my talk, I will pick out one or two examples from among these riches, with the hope of convincing the audience that Diophantus is not only the father of algebra, but the grandfather of birational geometry as well.

Colloquium coordinators are Prof.dr. A.J. van der Schaft ( a.j.van.der.schaft rug.nl ) and Dr. A.V. Kiselev (e-mail: a.v.kiselev rug.nl )

http://www.rug.nl/research/jbi/news/colloquia/mathematics-colloquia/