Dynamical Aspects of Teichmuller Theory: SL(2,R)-Action on Moduli Spaces of Flat Surfaces

Carlos Matheus Silva Santos - Collection Yellow Sale 2023

122 pages, parution le 19/07/2018

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Résumé

This book is a remarkable contribution to the literature on dynamical systems and geometry.

The author is an internationally recognized expert in dynamical systems with a talent to explain topics that is rarely found in the field.

This book is a remarkable contribution to the literature on dynamical systems and geometry. It consists of a selection of work in current research on Teichmuller dynamics, a field that has continued to develop rapidly in the past decades. After a comprehensive introduction, the author investigates the dynamics of the Teichmuller flow, presenting several self-contained chapters, each addressing a different aspect on the subject. The author includes innovative expositions, all the while solving open problems, constructing examples, and supplementing with illustrations. This book is a rare find in the field with its guidance and support for readers through the complex content of moduli spaces and Teichmuller Theory.

The author is an internationally recognized expert in dynamical systems with a talent to explain topics that is rarely found in the field. He has created a text that would benefit specialists in, not only dynamical systems and geometry, but also Lie theory and number theory.

Introduction.- Proof of the Eskin-Kontsevich-Zorich Regularity Conjecture.- Arithmetic Teichmuller Curves with Complementary Series.- Some Finiteness Results for Algebraically Primitive Teichmuller Curves.- Simplicity of Lyapunov Exponents of Arithmetic Teichmuller Curves.- An Example of Quaternionic Kontsevich-Zorich Monodromy Group.Carlos Matheus Silva Santos is a Brazilian mathematician who is an expert in the field of dynamical systems. He currently works at the Centre national de la recherche scientifique (CNRS), while teaching at both Ecole Polytechnique and Universite Paris 13. Additionally, he has organized various conferences in Paris and Rio de Janiero on the topic of dynamical systems.