Transcendental methods of algebraic/complex geometry in hyperbolic geometry

• Grant number: 16/15786-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2016
• End date: September 30, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Alexandre Ananin
• Grantee: Felipe Espreafico Guelerman Ramos
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Transcendental methods of algebraic/complex geometry are becoming more and more efficient in hyperbolic geometry (see, for instance, the recent scientific events dedicated to such interplay: "Algebraic geometry and hyperbolic geometry - new connections", "Hyperbolicity 2015", "Hyperbolic geometry and dynamics", "Monge-Ampere equation and Calabi-Yau manifolds"). The goal of the project is to prepare the student to this new direction in hyperbolic geometry through the study of selected topics in measure theory, complex analysis, Riemann surfaces, and algebraic/complex geometry.