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This volume contains 17 surveys that cover many recent developments in Discrete Geometry and related fields. Besides presenting the state-of-the-art of classical research subjects like packing and covering, it also offers an introduction to new topological, algebraic and computational methods in this very active research field. The readers will find a variety of modern topics and many fascinating open problems that may serve as starting points for research.

Geometry. --- Mathematics --- Euclid's Elements --- Discrete groups. --- Combinatorics. --- Topology. --- Convex and Discrete Geometry. --- Polytopes. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Combinatorics --- Algebra --- Mathematical analysis --- Groups, Discrete --- Infinite groups --- Discrete mathematics --- Convex geometry . --- Discrete geometry. --- Hyperspace --- Topology --- Combinatorial geometry --- Convex geometry. --- Discrete mathematics. --- Discrete Mathematics. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis

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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,.