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Book Synopsis Positive Gaussian Kernels Also Have Gaussian Minimizers by : Franck Barthe
Download or read book Positive Gaussian Kernels Also Have Gaussian Minimizers written by Franck Barthe and published by American Mathematical Society. This book was released on 2022-04-08 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
This book collects the lecture notes of the Summer School on Convex Geometry, held in Cetraro, Italy, from August 30th to September 3rd, 2021. Convex geometry is a very active area in mathematics with a solid tradition and a promising future. Its main objects of study are convex bodies, that is, compact and convex subsets of n-dimensional Euclidean space. The so-called Brunn--Minkowski theory currently represents the central part of convex geometry. The Summer School provided an introduction to various aspects of convex geometry: The theory of valuations, including its recent developments concerning valuations on function spaces; geometric and analytic inequalities, including those which come from the Lp Brunn--Minkowski theory; geometric and analytic notions of duality, along with their interplay with mass transportation and concentration phenomena; symmetrizations, which provide one of the main tools to many variational problems (not only in convex geometry). Each of these parts is represented by one of the courses given during the Summer School and corresponds to one of the chapters of the present volume. The initial chapter contains some basic notions in convex geometry, which form a common background for the subsequent chapters. The material of this book is essentially self-contained and, like the Summer School, is addressed to PhD and post-doctoral students and to all researchers approaching convex geometry for the first time.
Book Synopsis Convex Geometry by : Shiri Artstein-Avidan
Download or read book Convex Geometry written by Shiri Artstein-Avidan and published by Springer Nature. This book was released on 2023-12-13 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the lecture notes of the Summer School on Convex Geometry, held in Cetraro, Italy, from August 30th to September 3rd, 2021. Convex geometry is a very active area in mathematics with a solid tradition and a promising future. Its main objects of study are convex bodies, that is, compact and convex subsets of n-dimensional Euclidean space. The so-called Brunn--Minkowski theory currently represents the central part of convex geometry. The Summer School provided an introduction to various aspects of convex geometry: The theory of valuations, including its recent developments concerning valuations on function spaces; geometric and analytic inequalities, including those which come from the Lp Brunn--Minkowski theory; geometric and analytic notions of duality, along with their interplay with mass transportation and concentration phenomena; symmetrizations, which provide one of the main tools to many variational problems (not only in convex geometry). Each of these parts is represented by one of the courses given during the Summer School and corresponds to one of the chapters of the present volume. The initial chapter contains some basic notions in convex geometry, which form a common background for the subsequent chapters. The material of this book is essentially self-contained and, like the Summer School, is addressed to PhD and post-doctoral students and to all researchers approaching convex geometry for the first time.
Book Synopsis Partial Compactification of Monopoles and Metric Asymptotics by : Chris Kottke
Download or read book Partial Compactification of Monopoles and Metric Asymptotics written by Chris Kottke and published by American Mathematical Society. This book was released on 2022-11-10 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Hypergeometric Functions Over Finite Fields by : Jenny Fuselier
Download or read book Hypergeometric Functions Over Finite Fields written by Jenny Fuselier and published by American Mathematical Society. This book was released on 2022-11-10 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Adiabatic Evolution and Shape Resonances by : Michael Hitrik
Download or read book Adiabatic Evolution and Shape Resonances written by Michael Hitrik and published by American Mathematical Society. This book was released on 2022-11-10 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Theta Functions on Varieties with Effective Anti-Canonical Class by : Mark Gross
Download or read book Theta Functions on Varieties with Effective Anti-Canonical Class written by Mark Gross and published by American Mathematical Society. This book was released on 2022-07-18 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
This book reflects general trends in the study of geometric aspects of functional analysis, understood in a broad sense. A classical theme in the local theory of Banach spaces is the study of probability measures in high dimension and the concentration of measure phenomenon. Here this phenomenon is approached from different angles, including through analysis on the Hamming cube, and via quantitative estimates in the Central Limit Theorem under thin-shell and related assumptions. Classical convexity theory plays a central role in this volume, as well as the study of geometric inequalities. These inequalities, which are somewhat in spirit of the Brunn-Minkowski inequality, in turn shed light on convexity and on the geometry of Euclidean space. Probability measures with convexity or curvature properties, such as log-concave distributions, occupy an equally central role and arise in the study of Gaussian measures and non-trivial properties of the heat flow in Euclidean spaces. Also discussed are interactions of this circle of ideas with linear programming and sampling algorithms, including the solution of a question in online learning algorithms using a classical convexity construction from the 19th century.
Book Synopsis Geometric Aspects of Functional Analysis by : Ronen Eldan
Download or read book Geometric Aspects of Functional Analysis written by Ronen Eldan and published by Springer Nature. This book was released on 2023-11-01 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reflects general trends in the study of geometric aspects of functional analysis, understood in a broad sense. A classical theme in the local theory of Banach spaces is the study of probability measures in high dimension and the concentration of measure phenomenon. Here this phenomenon is approached from different angles, including through analysis on the Hamming cube, and via quantitative estimates in the Central Limit Theorem under thin-shell and related assumptions. Classical convexity theory plays a central role in this volume, as well as the study of geometric inequalities. These inequalities, which are somewhat in spirit of the Brunn-Minkowski inequality, in turn shed light on convexity and on the geometry of Euclidean space. Probability measures with convexity or curvature properties, such as log-concave distributions, occupy an equally central role and arise in the study of Gaussian measures and non-trivial properties of the heat flow in Euclidean spaces. Also discussed are interactions of this circle of ideas with linear programming and sampling algorithms, including the solution of a question in online learning algorithms using a classical convexity construction from the 19th century.
Book Synopsis Intrinsic Approach to Galois Theory of $q$-Difference Equations by : Lucia Di Vizio
Download or read book Intrinsic Approach to Galois Theory of $q$-Difference Equations written by Lucia Di Vizio and published by American Mathematical Society. This book was released on 2022-08-31 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria by : Jean-François Chassagneux
Download or read book A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria written by Jean-François Chassagneux and published by American Mathematical Society. This book was released on 2022-11-10 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Coefficient Systems on the Bruhat-Tits Building and Pro-$p$ Iwahori-Hecke Modules by : Jan Kohlhaase
Download or read book Coefficient Systems on the Bruhat-Tits Building and Pro-$p$ Iwahori-Hecke Modules written by Jan Kohlhaase and published by American Mathematical Society. This book was released on 2022-08-31 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
