Selected Works Of Oded Schramm

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Selected Works of Oded Schramm

Itai Benjamini,Olle Häggström
Selected Works of Oded Schramm Book PDF

Author : Itai Benjamini,Olle Häggström
Publisher : Springer Science & Business Media
Page : 1199 pages
File Size : 44,6 Mb
Release : 2011-08-12
Category : Mathematics
ISBN : 9781441996756

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Selected Works of Oded Schramm by Itai Benjamini,Olle Häggström Pdf

This volume is dedicated to the memory of the late Oded Schramm (1961-2008), distinguished mathematician. Throughout his career, Schramm made profound and beautiful contributions to mathematics that will have a lasting influence. In these two volumes, Editors Itai Benjamini and Olle Häggström have collected some of his papers, supplemented with three survey papers by Steffen Rohde, Häggström and Cristophe Garban that further elucidate his work. The papers within are a representative collection that shows the breadth, depth, enthusiasm and clarity of his work, with sections on Geometry, Noise Sensitivity, Random Walks and Graph Limits, Percolation, and finally Schramm-Loewner Evolution. An introduction by the Editors and a comprehensive bibliography of Schramm's publications complete the volume. The book will be of especial interest to researchers in probability and geometry, and in the history of these subjects.

Unimodularity in Randomly Generated Graphs

Florian Sobieczky
Unimodularity in Randomly Generated Graphs Book PDF

Author : Florian Sobieczky
Publisher : American Mathematical Soc.
Page : 211 pages
File Size : 52,9 Mb
Release : 2018-11-20
Category : Graph theory
ISBN : 9781470439149

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Unimodularity in Randomly Generated Graphs by Florian Sobieczky Pdf

This volume contains the proceedings of the AMS Special Session on Unimodularity in Randomly Generated Graphs, held from October 8–9, 2016, in Denver, Colorado. Unimodularity, a term initially used in locally compact topological groups, is one of the main examples in which the generalization from groups to graphs is successful. The “randomly generated graphs”, which include percolation graphs, random Erdős–Rényi graphs, and graphings of equivalence relations, are much easier to describe if they result as random objects in the context of unimodularity, with respect to either a vertex-transient “host”-graph or a probability measure. This volume tries to give an impression of the various fields in which the notion currently finds strong development and application: percolation theory, point processes, ergodic theory, and dynamical systems.

In the Tradition of Thurston

Ken’ichi Ohshika,Athanase Papadopoulos
In the Tradition of Thurston Book PDF

Author : Ken’ichi Ohshika,Athanase Papadopoulos
Publisher : Springer Nature
Page : 724 pages
File Size : 55,8 Mb
Release : 2020-12-07
Category : Mathematics
ISBN : 9783030559281

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In the Tradition of Thurston by Ken’ichi Ohshika,Athanase Papadopoulos Pdf

This book consists of 16 surveys on Thurston's work and its later development. The authors are mathematicians who were strongly influenced by Thurston's publications and ideas. The subjects discussed include, among others, knot theory, the topology of 3-manifolds, circle packings, complex projective structures, hyperbolic geometry, Kleinian groups, foliations, mapping class groups, Teichmüller theory, anti-de Sitter geometry, and co-Minkowski geometry. The book is addressed to researchers and students who want to learn about Thurston’s wide-ranging mathematical ideas and their impact. At the same time, it is a tribute to Thurston, one of the greatest geometers of all time, whose work extended over many fields in mathematics and who had a unique way of perceiving forms and patterns, and of communicating and writing mathematics.

Extended Abstracts Fall 2019

Evgeny Abakumov,Anton Baranov,Alexander Borichev,Konstantin Fedorovskiy,Joaquim Ortega-Cerdà
Extended Abstracts Fall 2019 Book PDF

Author : Evgeny Abakumov,Anton Baranov,Alexander Borichev,Konstantin Fedorovskiy,Joaquim Ortega-Cerdà
Publisher : Springer Nature
Page : 223 pages
File Size : 50,9 Mb
Release : 2021-11-19
Category : Mathematics
ISBN : 9783030744175

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Extended Abstracts Fall 2019 by Evgeny Abakumov,Anton Baranov,Alexander Borichev,Konstantin Fedorovskiy,Joaquim Ortega-Cerdà Pdf

This book collects the abstracts of the mini-courses and lectures given during the Intensive Research Program “Spaces of Analytic Functions: Approximation, Interpolation, Sampling” which was held at the Centre de Recerca Matemàtica (Barcelona) in October–December, 2019. The topics covered in this volume are approximation, interpolation and sampling problems in spaces of analytic functions, their applications to spectral theory, Gabor analysis and random analytic functions. In many places in the book, we see how a problem related to one of the topics is tackled with techniques and ideas coming from another. The book will be of interest for specialists in Complex Analysis, Function and Operator theory, Approximation theory, and their applications, but also for young people starting their research in these areas.

Percolation on Triangulations: A Bijective Path to Liouville Quantum Gravity

Olivier Bernardi,Nina Holden,Xin Sun
Percolation on Triangulations A Bijective Path to Liouville Quantum Gravity Book PDF

Author : Olivier Bernardi,Nina Holden,Xin Sun
Publisher : American Mathematical Society
Page : 188 pages
File Size : 45,6 Mb
Release : 2023-09-27
Category : Mathematics
ISBN : 9781470466992

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Percolation on Triangulations: A Bijective Path to Liouville Quantum Gravity by Olivier Bernardi,Nina Holden,Xin Sun Pdf

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Theorems of the 21st Century

Bogdan Grechuk
Theorems of the 21st Century Book PDF

Author : Bogdan Grechuk
Publisher : Springer
Page : 446 pages
File Size : 53,6 Mb
Release : 2019-06-15
Category : Mathematics
ISBN : 9783030190965

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Theorems of the 21st Century by Bogdan Grechuk Pdf

This book consists of short descriptions of 106 mathematical theorems, which belong to the great achievements of 21st century mathematics but require relatively little mathematical background to understand their formulation and appreciate their importance. The selected theorems of this volume, chosen from the famous Annals of Mathematics journal, cover a broad range of topics from across mathematics. Each theorem description is essentially self-contained, can be read independently of the others, and requires as little preliminary knowledge as possible. Although the sections often start with an informal discussion and toy examples, all the necessary definitions are included and each description culminates in the precise formulation of the corresponding theorem. Filling the gap between surveys written for mathematicians and popular mathematics, this book is intended for readers with a keen interest in contemporary mathematics.

The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles

E. J. Janse van Rensburg
The Statistical Mechanics of Interacting Walks Polygons Animals and Vesicles Book PDF

Author : E. J. Janse van Rensburg
Publisher : OUP Oxford
Page : 640 pages
File Size : 45,7 Mb
Release : 2015-05-14
Category : Mathematics
ISBN : 9780191644672

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The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles by E. J. Janse van Rensburg Pdf

The self-avoiding walk is a classical model in statistical mechanics, probability theory and mathematical physics. It is also a simple model of polymer entropy which is useful in modelling phase behaviour in polymers. This monograph provides an authoritative examination of interacting self-avoiding walks, presenting aspects of the thermodynamic limit, phase behaviour, scaling and critical exponents for lattice polygons, lattice animals and surfaces. It also includes a comprehensive account of constructive methods in models of adsorbing, collapsing, and pulled walks, animals and networks, and for models of walks in confined geometries. Additional topics include scaling, knotting in lattice polygons, generating function methods for directed models of walks and polygons, and an introduction to the Edwards model. This essential second edition includes recent breakthroughs in the field, as well as maintaining the older but still relevant topics. New chapters include an expanded presentation of directed models, an exploration of methods and results for the hexagonal lattice, and a chapter devoted to the Monte Carlo methods.

A Journey Through Discrete Mathematics

Martin Loebl,Jaroslav Nešetřil,Robin Thomas
A Journey Through Discrete Mathematics Book PDF

Author : Martin Loebl,Jaroslav Nešetřil,Robin Thomas
Publisher : Springer
Page : 810 pages
File Size : 54,9 Mb
Release : 2017-10-11
Category : Computers
ISBN : 9783319444796

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A Journey Through Discrete Mathematics by Martin Loebl,Jaroslav Nešetřil,Robin Thomas Pdf

This collection of high-quality articles in the field of combinatorics, geometry, algebraic topology and theoretical computer science is a tribute to Jiří Matoušek, who passed away prematurely in March 2015. It is a collaborative effort by his colleagues and friends, who have paid particular attention to clarity of exposition – something Jirka would have approved of. The original research articles, surveys and expository articles, written by leading experts in their respective fields, map Jiří Matoušek’s numerous areas of mathematical interest.

Collected Works of William P. Thurston with Commentary

Benson Farb,David Gabai,Steven P. Kerckhoff
Collected Works of William P Thurston with Commentary Book PDF

Author : Benson Farb,David Gabai,Steven P. Kerckhoff
Publisher : American Mathematical Society
Page : 629 pages
File Size : 48,8 Mb
Release : 2022-07-19
Category : Mathematics
ISBN : 9781470463908

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Collected Works of William P. Thurston with Commentary by Benson Farb,David Gabai,Steven P. Kerckhoff Pdf

William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. His emphasis on understanding and imagination in mathematical learning and thinking are integral elements of his distinctive legacy. This four-part collection brings together in one place Thurston's major writings, many of which are appearing in publication for the first time. Volumes I–III contain commentaries by the Editors. Volume IV includes a preface by Steven P. Kerckhoff. Volume III contains William Thurston's papers on dynamics and computer science, and papers written for general audiences. Additional miscellaneous papers are also included, such as his 1967 New College undergraduate thesis, which foreshadows his later work.

Complex Analysis

Prem K. Kythe
Complex Analysis Book PDF

Author : Prem K. Kythe
Publisher : CRC Press
Page : 343 pages
File Size : 52,9 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781498718998

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Complex Analysis by Prem K. Kythe Pdf

Complex Analysis: Conformal Inequalities and the Bieberbach Conjecture discusses the mathematical analysis created around the Bieberbach conjecture, which is responsible for the development of many beautiful aspects of complex analysis, especially in the geometric-function theory of univalent functions. Assuming basic knowledge of complex analysis and differential equations, the book is suitable for graduate students engaged in analytical research on the topics and researchers working on related areas of complex analysis in one or more complex variables. The author first reviews the theory of analytic functions, univalent functions, and conformal mapping before covering various theorems related to the area principle and discussing Löwner theory. He then presents Schiffer’s variation method, the bounds for the fourth and higher-order coefficients, various subclasses of univalent functions, generalized convexity and the class of α-convex functions, and numerical estimates of the coefficient problem. The book goes on to summarize orthogonal polynomials, explore the de Branges theorem, and address current and emerging developments since the de Branges theorem.

Brownian Motion

Peter Mörters,Yuval Peres
Brownian Motion Book PDF

Author : Peter Mörters,Yuval Peres
Publisher : Cambridge University Press
Page : 128 pages
File Size : 52,9 Mb
Release : 2010-03-25
Category : Mathematics
ISBN : 9781139486576

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Brownian Motion by Peter Mörters,Yuval Peres Pdf

This eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine properties of Brownian paths. The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration is introduced as a tool and an accessible treatment of the potential theory of Brownian motion clears the path for an extensive treatment of intersections of Brownian paths. An investigation of exceptional points on the Brownian path and an appendix on SLE processes, by Oded Schramm and Wendelin Werner, lead directly to recent research themes.

Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs

Emanuel Indrei,Diego Marcon,Levon Nurbekyan
Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs Book PDF

Author : Emanuel Indrei,Diego Marcon,Levon Nurbekyan
Publisher : American Mathematical Society
Page : 148 pages
File Size : 41,8 Mb
Release : 2023-01-09
Category : Mathematics
ISBN : 9781470466527

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Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs by Emanuel Indrei,Diego Marcon,Levon Nurbekyan Pdf

This volume contains the proceedings of the virtual conference on Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs, held from February 28–March 1, 2021, and hosted by Purdue University, West Lafayette, IN. The mathematical content of this volume is at the intersection of viscosity theory, Fourier analysis, mass transport theory, fractional elliptic theory, and geometric analysis. The reader will encounter, among others, the following topics: the principal-agent problem; Maxwell's equations; Liouville-type theorems for fully nonlinear elliptic equations; a doubly monotone flow for constant width bodies; and the edge dislocations problem for crystals that describes the equilibrium configurations by a nonlocal fractional Laplacian equation.

Noise Sensitivity of Boolean Functions and Percolation

Christophe Garban,Jeffrey E. Steif
Noise Sensitivity of Boolean Functions and Percolation Book PDF

Author : Christophe Garban,Jeffrey E. Steif
Publisher : Cambridge University Press
Page : 223 pages
File Size : 54,6 Mb
Release : 2015
Category : Computers
ISBN : 9781107076433

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Noise Sensitivity of Boolean Functions and Percolation by Christophe Garban,Jeffrey E. Steif Pdf

This is the first book to cover the theory of noise sensitivity of Boolean functions with particular emphasis on critical percolation.

What's Happening in the Mathematical Sciences

Barry Cipra
What s Happening in the Mathematical Sciences Book PDF

Author : Barry Cipra
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 49,6 Mb
Release : 2024-07-02
Category : Science
ISBN : 0821890433

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What's Happening in the Mathematical Sciences by Barry Cipra Pdf

Mathematicians like to point out that mathematics is universal. In spite of this, most people continue to view it as either mundane (balancing a checkbook) or mysterious (cryptography). This fifth volume of the What's Happening series contradicts that view by showing that mathematics is indeed found everywhere-in science, art, history, and our everyday lives. Here is some of what you'll find in this volume: Mathematics and Science Mathematical biology: Mathematics was key tocracking the genetic code. Now, new mathematics is needed to understand the three-dimensional structure of the proteins produced from that code. Celestial mechanics and cosmology: New methods have revealed a multitude of solutions to the three-body problem. And other new work may answer one of cosmology'smost fundamental questions: What is the size and shape of the universe? Mathematics and Everyday Life Traffic jams: New models are helping researchers understand where traffic jams come from-and maybe what to do about them! Small worlds: Researchers have found a short distance from theory to applications in the study of small world networks. Elegance in Mathematics Beyond Fermat's Last Theorem: Number theorists are reaching higher ground after Wiles' astounding 1994 proof: new developments inthe elegant world of elliptic curves and modular functions. The Millennium Prize Problems: The Clay Mathematics Institute has offered a million dollars for solutions to seven important and difficult unsolved problems. These are just some of the topics of current interest that are covered in thislatest volume of What's Happening in the Mathematical Sciences. The book has broad appeal for a wide spectrum of mathematicians and scientists, from high school students through advanced-level graduates and researchers.

Conformal Invariants

Lars Valerian Ahlfors
Conformal Invariants Book PDF

Author : Lars Valerian Ahlfors
Publisher : American Mathematical Soc.
Page : 177 pages
File Size : 41,8 Mb
Release : 2010-11-17
Category : Mathematics
ISBN : 9780821852705

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Conformal Invariants by Lars Valerian Ahlfors Pdf

Most conformal invariants can be described in terms of extremal properties. Conformal invariants and extremal problems are therefore intimately linked and form together the central theme of this classic book which is primarily intended for students with approximately a year's background in complex variable theory. The book emphasizes the geometric approach as well as classical and semi-classical results which Lars Ahlfors felt every student of complex analysis should know before embarking on independent research. At the time of the book's original appearance, much of this material had never appeared in book form, particularly the discussion of the theory of extremal length. Schiffer's variational method also receives special attention, and a proof of $\vert a_4\vert \leq 4$ is included which was new at the time of publication. The last two chapters give an introduction to Riemann surfaces, with topological and analytical background supplied to support a proof of the uniformization theorem. Included in this new reprint is a Foreword by Peter Duren, F. W. Gehring, and Brad Osgood, as well as an extensive errata. ... encompasses a wealth of material in a mere one hundred and fifty-one pages. Its purpose is to present an exposition of selected topics in the geometric theory of functions of one complex variable, which in the author's opinion should be known by all prospective workers in complex analysis. From a methodological point of view the approach of the book is dominated by the notion of conformal invariant and concomitantly by extremal considerations. ... It is a splendid offering. --Reviewed for Math Reviews by M. H. Heins in 1975