Joint Number Theory/Logic Seminar: Two models for the hyperbolic plane and existence of the Poincare metric on compact Riemann surfaces

Seminar series

Date

Thu, 12 May 2016
16:00

Location

Speaker

Norbert A'Campo

Organisation

Basel

An implicite definition for the hyperbolic plane $H=H_I$ is in:

${\rm Spec}(\mathbb{R}[X]) = H_I \setunion \mathbb{R}$.

All geometric hyperbolic features will follow from this definition in an elementary way.

A second definition is

$H=H_J=\{J \in {\rm End}(R^2) \mid J^2=-Id, dx \wedge dy(u,Ju) \geq 0 \}$.

Working with $H=H_J$ allows to prove rather directly main theorems about Riemann surfaces.