Abstract: A hyperelliptic curve of genus g is a degree 2 cover of the Riemann sphere with 2g+2 ramification points. We say that the two preimages, p and q, of the point at infinity is a torsion pair if there exists a function with a unique zero at p and a unique pole at q.
The study of these curves with torsion has a long and rich history. In this talk, I want to present, in the case of genus 2 curves, some of their relations with other objects, including: differentials on Riemann surfaces, continued fractions, Teichmüller curves and Pell-Abel equation.
Bio: Quentin GENDRON, Researcher in Autonomous National University of Mexico (UNAM) in Mexico City.
After having studying in France, Quentin graduated from the University of Frankfurt in Germany on a topic related to deformations of abelian differentials on Riemann surfaces. After some postdocs in Germany and in Mexico, Quentin became professor at the Autonomous National University of Mexico (UNAM) in Mexico City.
Mathematical interests: Relationship between differentials on Riemann surfaces and any other topic.
