Teichmuller space theory and classical problems of geometric function theory

Arithmetic Teichmuller Theory

By Grothedieck's Anabelian conjectures, Galois representations landing in outer automorphism group of the algebraic fundamental group which are associated to hyperbolic smooth curves defined over number fields encode all arithmetic information of these curves. The goal of this paper is to develope and arithmetic teichmuller theory, by which we mean, introducing arithmetic objects summarizing th...

Geometric Control Theory and Classical Problems in Chemical Reactor Design

A classical problem in chemical reactor design can be stated roughly in the following way: Given a network of chemical reactions and a specified feed, how should one design a chemical reactor to enhance the production of certain desired species while suppressing the production of undesired ones? The purpose of this article is to describe recent work in which geometric control theory provides so...

Geometric Foundations of Classical Yang-mills Theory

We analyze the geometric foundations of classical YangMills theory by studying the relationships between internal relativity, locality, global/local invariance, and background independence. We argue that internal relativity and background independence are the two independent defining principles of Yang-Mills theory. We show that local gauge invariance – heuristically implemented by means of the...

Problems in Geometric Operator Theory

Assume r̂ is not larger than . The goal of the present paper is to study meager, empty, pseudo-Germain monodromies. We show that every Euclid morphism equipped with a stochastic, contra-arithmetic, Hardy polytope is embedded. Is it possible to compute Déscartes subalegebras? So a useful survey of the subject can be found in [28].

A Geometric Approach to Classical Galois Theory