Author : G. O. Jones
Publisher : Cambridge University Press
Page : 235 pages
File Size : 45,30 MB
Release : 2015-08-13
Category : Mathematics
ISBN : 1107462495
This book brings the researcher up to date with recent applications of mathematical logic to number theory.
Author : Carolina Araujo
Publisher : Cambridge University Press
Page : 452 pages
File Size : 18,52 MB
Release : 2023-06-30
Category : Mathematics
ISBN : 1009239651
Algebraic varieties are shapes defined by polynomial equations. Smooth Fano threefolds are a fundamental subclass that can be thought of as higher-dimensional generalizations of ordinary spheres. They belong to 105 irreducible deformation families. This book determines whether the general element of each family admits a Kähler–Einstein metric (and for many families, for all elements), addressing a question going back to Calabi 70 years ago. The book's solution exploits the relation between these metrics and the algebraic notion of K-stability. Moreover, the book presents many different techniques to prove the existence of a Kähler–Einstein metric, containing many additional relevant results such as the classification of all Kähler–Einstein smooth Fano threefolds with infinite automorphism groups and computations of delta-invariants of all smooth del Pezzo surfaces. This book will be essential reading for researchers and graduate students working on algebraic geometry and complex geometry.
Author : Joppe Bos
Publisher :
Page : 402 pages
File Size : 34,68 MB
Release : 2021-12-09
Category : Language Arts & Disciplines
ISBN : 1108848427
The area of computational cryptography is dedicated to the development of effective methods in algorithmic number theory that improve implementation of cryptosystems or further their cryptanalysis. This book is a tribute to Arjen K. Lenstra, one of the key contributors to the field, on the occasion of his 65th birthday, covering his best-known scientific achievements in the field. Students and security engineers will appreciate this no-nonsense introduction to the hard mathematical problems used in cryptography and on which cybersecurity is built, as well as the overview of recent advances on how to solve these problems from both theoretical and practical applied perspectives. Beginning with polynomials, the book moves on to the celebrated Lenstra-Lenstra-Lovász lattice reduction algorithm, and then progresses to integer factorization and the impact of these methods to the selection of strong cryptographic keys for usage in widely used standards.
Author : Jan-Hendrik Evertse
Publisher : Cambridge University Press
Page : 242 pages
File Size : 19,87 MB
Release : 2022-04-28
Category : Mathematics
ISBN : 1009050036
This book provides the first thorough treatment of effective results and methods for Diophantine equations over finitely generated domains. Compiling diverse results and techniques from papers written in recent decades, the text includes an in-depth analysis of classical equations including unit equations, Thue equations, hyper- and superelliptic equations, the Catalan equation, discriminant equations and decomposable form equations. The majority of results are proved in a quantitative form, giving effective bounds on the sizes of the solutions. The necessary techniques from Diophantine approximation and commutative algebra are all explained in detail without requiring any specialized knowledge on the topic, enabling readers from beginning graduate students to experts to prove effective finiteness results for various further classes of Diophantine equations.
Author : Fosco Loregian
Publisher : Cambridge University Press
Page : 331 pages
File Size : 14,5 MB
Release : 2021-07-22
Category : Mathematics
ISBN : 1108746128
This easy-to-cite handbook gives the first systematic treatment of the (co)end calculus in category theory and its applications.
Author : Scott Balchin
Publisher : Cambridge University Press
Page : 358 pages
File Size : 48,26 MB
Release : 2021-11-18
Category : Mathematics
ISBN : 1108950671
This volume contains eight research papers inspired by the 2019 'Equivariant Topology and Derived Algebra' conference, held at the Norwegian University of Science and Technology, Trondheim in honour of Professor J. P. C. Greenlees' 60th birthday. These papers, written by experts in the field, are intended to introduce complex topics from equivariant topology and derived algebra while also presenting novel research. As such this book is suitable for new researchers in the area and provides an excellent reference for established researchers. The inter-connected topics of the volume include: algebraic models for rational equivariant spectra; dualities and fracture theorems in chromatic homotopy theory; duality and stratification in tensor triangulated geometry; Mackey functors, Tambara functors and connections to axiomatic representation theory; homotopy limits and monoidal Bousfield localization of model categories.
Author : Masaki Kashiwara
Publisher : Cambridge University Press
Page : 119 pages
File Size : 15,29 MB
Release : 2016-05-26
Category : Mathematics
ISBN : 1316613453
A unified treatment of the Riemann-Hilbert correspondence for (not necessarily regular) holonomic D-modules using indsheaves.
Author : Manfred Stoll
Publisher : Cambridge University Press
Page : 243 pages
File Size : 50,59 MB
Release : 2016-06-30
Category : Mathematics
ISBN : 1107541484
A detailed treatment of potential theory on the real hyperbolic ball and half-space aimed at researchers and graduate students.
Author : C. T. J. Dodson
Publisher : Cambridge University Press
Page : 315 pages
File Size : 42,94 MB
Release : 2016
Category : Mathematics
ISBN : 1316601951
A new approach to studying Fréchet geometry using projective limits of geometrical objects modelled on Banach spaces.
Author : Thomas J. Bridges
Publisher : Cambridge University Press
Page : 299 pages
File Size : 35,73 MB
Release : 2016-02-04
Category : Science
ISBN : 1316558940
In the summer of 2014 leading experts in the theory of water waves gathered at the Newton Institute for Mathematical Sciences in Cambridge for four weeks of research interaction. A cross-section of those experts was invited to give introductory-level talks on active topics. This book is a compilation of those talks and illustrates the diversity, intensity, and progress of current research in this area. The key themes that emerge are numerical methods for analysis, stability and simulation of water waves, transform methods, rigorous analysis of model equations, three-dimensionality of water waves, variational principles, shallow water hydrodynamics, the role of deterministic and random bottom topography, and modulation equations. This book is an ideal introduction for PhD students and researchers looking for a research project. It may also be used as a supplementary text for advanced courses in mathematics or fluid dynamics.
