Ángel David Ríos Ortiz: Reconstruction of Algebraic Curves From Analytic Presentations

Abstract

Riemann surfaces have three different incarnations: geometric, analytic, and algebraic. Each definition has its advantages and is suitable for different purposes. Although the passage from the geometric to the algebraic side is in theory possible, it is inherently transcendental. In order to make this passage effective (i.e. with a computer) we need to choose the right geometric and algebraic presentations. I will present joint work with Samantha Fairchild where we compute (an approximation of) the defining equations of algebraic curves coming from geometric group theory.