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This book focuses on developments in complex dynamical systems and geometric function theory over the past decade, showing strong links with other areas of mathematics and the natural sciences. Traditional methods and approaches surface in physics and in the life and engineering sciences with increasing frequency – the Schramm‐Loewner evolution, Laplacian growth, and quadratic differentials are just a few typical examples. This book provides a representative overview of these processes and collects open problems in the various areas, while at the same time showing where and how each particular topic evolves. This volume is dedicated to the memory of Alexander Vasiliev.

Mathematical analysis. --- Differentiable dynamical systems. --- Mathematics. --- Functional analysis. --- Functions of complex variables. --- Integral transforms. --- Operational calculus. --- Operator theory. --- Differential equations. --- Functions of a Complex Variable. --- Several Complex Variables and Analytic Spaces. --- Ordinary Differential Equations. --- Integral Transforms, Operational Calculus. --- Functional Analysis. --- Operator Theory. --- 517.91 Differential equations --- Differential equations --- Functional analysis --- Operational calculus --- Electric circuits --- Integral equations --- Transform calculus --- Transformations (Mathematics) --- Complex variables --- Elliptic functions --- Functions of real variables --- Functional calculus --- Calculus of variations --- Functional equations --- Math --- Science --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- 517.1 Mathematical analysis --- Mathematical analysis --- Differential equations, partial. --- Differential Equations. --- Integral Transforms. --- Partial differential equations

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"In recent years, the interaction between harmonic analysis and convex geometry has increased which has resulted in solutions to several long-standing problems. This collection is based on the topics discussed during the Research Semester on Harmonic Analysis and Convexity at the Institute for Computational and Experimental Research in Mathematics in Providence RI in Fall 2022.The volume brings together experts working in related fields to report on the status of major problems in the area including the isomorphic Busemann-Petty and slicing problems for arbitrary measures, extremal problems for Fourier extension and extremal problems for classical singular integrals of martingale type, among others.The interaction between harmonic analysis and convex geometry has increased which has resulted in solutions to several long-standing problems. This book brings together experts in both areas, along with researchers working in related applied fields."--Provided by publisher.

Convex geometry. --- Harmonic analysis. --- harmonic analysis, convex geometry, geometric tomography, geometric properties, optimal algorithms,.