Series: De Gruyter Textbook
De Gruyter | 2020
This is a clear, rigorous and self-contained introduction to PDEs for a semester-based course on the topic. For the sake of smooth exposition, the book keeps the amount of applications to a minimum, focusing instead on the theoretical essentials and problem solving. The result is an agile compendium of theorems and methods - the ideal companion for any student tackling PDEs for the first time.
Comprehensible introduction to the theory of PDEs.
Reader-friendly rigour throughout.
Systematic use of modern mathematical software.
EMS Series of Congress Reports
ISBN print 978-3-03719-198-9, ISBN online 978-3-03719-698-4
DOI 10.4171/198
May 2020, 473 pages, hardcover, 17 x 24 cm.
This volume contains research and survey articles on Drinfeld modules, Anderson t-modules and t-motives. Much material that had not been easily accessible in the literature is presented here, for example the cohomology theories and Pink’s theory of Hodge structures attached to Drinfeld modules and t-motives. Also included are survey articles on the function field analogue of Fontaine’s theory of p-adic crystalline Galois representations and on transcendence methods over function fields, encompassing the theories of Frobenius difference equations, automata theory, and Mahler’s method. In addition, this volume contains a small number of research articles on function field Iwasawa theory, 1-t-motifs, and multizeta values.
This book is a useful source for learning important techniques and an effective reference for all researchers working in or interested in the area of function field arithmetic, from graduate students to established experts.
Keywords: Drinfeld modules, t-motives, Anderson t-modules, transcendence, Hodge-Pink-structures
Surveys in Differential Geometry Volume 23 (2018)
Published: 15 June 2020
Publisher: International Press of Boston, Inc.
Hardcover
346 pages
This is the first of two volumes consisting of lectures given at conferences held in 2019 to celebrate the seventieth birthday of Shing-Tung Yau: at Harvard University (May), at the University of Rome (May/June), at the Chinese University of Hong Kong (June), at the 8th ICCM Congress at Tsinghua University (June), at Lehigh University in Pennsylvania (November), and elsewhere.
Included here are: Werner Ballmann on “Bottom of spectra and coverings;” Robert J. Berman with “An invitation to Kahler?Einstein metrics and random point processes”; Duong H. Phong on “Unification of the Kahler?Ricci and anomaly flows”; Cumrun Vafa on “SCFTs, holography, and topological strings”; Stephen S.-T. Yau on “Recent results on k-th Yau algebras over simple elliptic singularities E~6”; Kefeng Liu on “Global methods of solving equations on manifolds”; Chuu-Lian Terng on “The geometric airy curve flow on Rn”; and Valentino Tosatti on “Collapsing Calabi?Yau manifolds.”
Hardcover ISBN: 9780444643056
Imprint: North Holland
Published Date: 10th January 2021
Page Count: 500
Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations. It includes basic ideas, analysis and applications of state-of-the-art fundamental algorithms for the approximation of geometric PDEs together with their impacts in a variety of fields within mathematics, science, and engineering.
About every aspect of computational geometric PDEs is discussed in this and a companion volume. Topics in this volume include stationary and time-dependent surface PDEs for geometric flows, large deformations of nonlinearly geometric plates and rods, level set and phase field methods and applications, free boundary problems, discrete Riemannian calculus and morphing, fully nonlinear PDEs including Monge-Ampere equations, and PDE constrained optimization
Each chapter is a complete essay at the research level but accessible to junior researchers and students. The intent is to provide a comprehensive description of algorithms and their analysis for a specific geometric PDE class, starting from basic concepts and concluding with interesting applications. Each chapter is thus useful as an introduction to a research area as well as a teaching resource, and provides numerous pointers to the literature for further reading
The authors of each chapter are world leaders in their field of expertise and skillful writers. This book is thus meant to provide an invaluable, readable and enjoyable account of computational geometric PDEs
1. Optimal control of geometric partial differential equations
Michael Hintermueller
2. Shape optimization
Gregoire Allaire
3. Total variation minimization
Antonin Chambolle
4. Numerical relativity
M. Holst
5. Numerical Simulation and Bench- marking of Drops and Bubbles
Stefan Turek
6. Optimal Transport
Quentin Merigot
7. Gradient flows
J. carrillo
8. Isogeometric Analysis
Giancarlo Sangalli
9. Liquid Crystals
Shaw Walker
This book seeks to describe the rapid development in recent decades of sieve methods able to detect prime numbers. The subject began with Eratosthenes in antiquity, took on new shape with Legendre’s form of the sieve, was substantially reworked by Ivan M. Vinogradov and Yuri V. Linnik, but came into its own with Robert C. Vaughan and important contributions from others, notably Roger Heath-Brown and Henryk Iwaniec. Prime-Detecting Sieves breaks new ground by bringing together several different types of problems that have been tackled with modern sieve methods and by discussing the ideas common to each, in particular the use of Type I and Type II information.
No other book has undertaken such a systematic treatment of prime-detecting sieves. Among the many topics Glyn Harman covers are primes in short intervals, the greatest prime factor of the sequence of shifted primes, Goldbach numbers in short intervals, the distribution of Gaussian primes, and the recent work of John Friedlander and Iwaniec on primes that are a sum of a square and a fourth power, and Heath-Brown’s work on primes represented as a cube plus twice a cube. This book contains much that is accessible to beginning graduate students, yet also provides insights that will benefit established researchers.
Series: London Mathematical Society Monographs
9780691202990
Published:
05/26/2020
Pages: 384
Size: 6.13 x 9.25 in.
Illus: 10 b/w illus. 9 tables.