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Complex analysis --- Univalent functions --- 51 --- Functions, Schlicht --- Functions, Simple --- Functions, Univalent --- Schlicht functions --- Simple functions --- Functions of complex variables --- Geometric function theory --- Mathematics --- 51 Mathematics --- Noyaux (analyse fonctionnelle) --- Kernel functions. --- Fonctions d'une variable complexe --- Fonctions univalentes

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The two parts of the present volume contain extended conference abstracts corresponding to selected talks given by participants at the "Conference on Geometric Analysis" (thirteen abstracts) and at the "Conference on Type Theory, Homotopy Theory and Univalent Foundations" (seven abstracts), both held at the Centre de Recerca Matemàtica (CRM) in Barcelona from July 1st to 5th, 2013, and from September 23th to 27th, 2013, respectively. Most of them are brief articles, containing preliminary presentations of new results not yet published in regular research journals. The articles are the result of a direct collaboration between active researchers in the area after working in a dynamic and productive atmosphere. The first part is about Geometric Analysis and Conformal Geometry; this modern field lies at the intersection of many branches of mathematics (Riemannian, Conformal, Complex or Algebraic Geometry, Calculus of Variations, PDE's, etc) and relates directly to the physical world, since many natural phenomena posses an intrinsic geometric content. The second part is about Type Theory, Homotopy Theory and Univalent Foundations. The book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active areas of research.

Geometry --- Mathematics --- Physical Sciences & Mathematics --- Geometry, Algebraic. --- Type theory. --- Homotopy theory. --- Univalent functions. --- Functions, Schlicht --- Functions, Simple --- Functions, Univalent --- Schlicht functions --- Simple functions --- Deformations, Continuous --- Algebraic geometry --- Mathematics. --- Differential geometry. --- Algebraic topology. --- Differential Geometry. --- Algebraic Topology. --- Functions of complex variables --- Geometric function theory --- Topology --- Logic, Symbolic and mathematical --- Global differential geometry. --- Geometry, Differential --- Differential geometry

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This book provides valuable insights into complex analysis, dynamical systems, geometric function theory and operator theory. Intended for a broad spectrum of readers, ranging from undergraduate and graduate mathematics students to active researchers, it offers extensive coverage of recent advances in geometric function theory, including the theory of starlike and spirallike functions with respect to a boundary point. Of particular interest is its treatment of continuous time semigroups, about which little has been previously known, emphasizing the use of generation theory for continuous dynamical systems. Such semigroups have important applications in such areas as composition operators, Markov stochastic processes, control theory and optimization. Readers will find in this book a systematic and detailed survey of linearization models for one-parameter continuous semigroups, functional equations, and the different classes of univalent functions which serve as intertwining mappings for these semigroups, along with their applications to various problems of complex dynamics.

Dynamics -- Statistical methods. --- Linear models (Statistics). --- Statistics. --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Calculus --- Differentiable dynamical systems. --- Linear models (Statistics) --- Univalent functions. --- Functional equations. --- Semigroups. --- Equations, Functional --- Functions, Schlicht --- Functions, Simple --- Functions, Univalent --- Schlicht functions --- Simple functions --- Models, Linear (Statistics) --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Mathematics. --- Difference equations. --- Dynamics. --- Ergodic theory. --- Functions of complex variables. --- System theory. --- Dynamical Systems and Ergodic Theory. --- Functions of a Complex Variable. --- Systems Theory, Control. --- Difference and Functional Equations. --- Functional analysis --- Group theory --- Functions of complex variables --- Geometric function theory --- Mathematical models --- Mathematical statistics --- Statistics --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Systems theory. --- Complex variables --- Elliptic functions --- Functions of real variables --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Systems, Theory of --- Systems science --- Science --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Philosophy