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Author : Gabriel Navarro
Publisher : Cambridge University Press
Page : 253 pages
File Size : 53,8 Mb
Release : 2018-04-26
Category : Mathematics
ISBN : 9781108428446
Presents contemporary character theory of finite groups from the basics to the state of the art, with new, refined proofs.
Author : Meinolf Geck,Gunter Malle
Publisher : Cambridge University Press
Page : 405 pages
File Size : 41,5 Mb
Release : 2020-02-27
Category : Mathematics
ISBN : 9781108489621
A comprehensive guide to the vast literature and range of results around Lusztig's character theory of finite groups of Lie type.
Author : Mark L. Lewis
Publisher : American Mathematical Soc.
Page : 194 pages
File Size : 53,9 Mb
Release : 2010-09-17
Category : Mathematics
ISBN : 9780821848272
This volume contains a collection of papers from the Conference on Character Theory of Finite Groups, held at the Universitat de Valencia, Spain, on June 3-5, 2009, in honor of I. Martin Isaacs. The topics include permutation groups, character theory, p-groups, and group rings. The research articles feature new results on large normal abelian subgroups of p-groups, construction of certain wreath products, computing idempotents in group algebras of finite groups, and using dual pairs to study representations of cross characteristic in classical groups. The expository articles present results on vertex subgroups, measuring theorems in permutation groups, the development of super character theory, and open problems in character theory.
Author : N.S. Narasimha Sastry,Manoj Kumar Yadav
Publisher : Springer
Page : 206 pages
File Size : 41,6 Mb
Release : 2018-09-21
Category : Mathematics
ISBN : 9789811320477
This book is a blend of recent developments in theoretical and computational aspects of group theory. It presents the state-of-the-art research topics in different aspects of group theory, namely, character theory, representation theory, integral group rings, the Monster simple group, computational algorithms and methods on finite groups, finite loops, periodic groups, Camina groups and generalizations, automorphisms and non-abelian tensor product of groups. Presenting a collection of invited articles by some of the leading and highly active researchers in the theory of finite groups and their representations and the Monster group, with a focus on computational aspects, this book is of particular interest to researchers in the area of group theory and related fields of mathematics.
Author : Francesco Maggi
Publisher : Cambridge University Press
Page : 317 pages
File Size : 52,6 Mb
Release : 2023-10-31
Category : Mathematics
ISBN : 9781009179706
A pedagogical introduction to the key ideas and theoretical foundation of optimal mass transport for a graduate course or self-study.
Author : Daniel Huybrechts
Publisher : Cambridge University Press
Page : 461 pages
File Size : 42,9 Mb
Release : 2023-06-30
Category : Mathematics
ISBN : 9781009280006
A detailed introduction to cubic hypersurfaces, applying diverse techniques to a central class of algebraic varieties.
Author : David Anderson,William Fulton
Publisher : Cambridge University Press
Page : 463 pages
File Size : 46,9 Mb
Release : 2023-11-30
Category : Mathematics
ISBN : 9781009349987
A graduate-level introduction to the core notions of equivariant cohomology, an indispensable tool in several areas of modern mathematics.
Author : Ariel Yadin
Publisher : Cambridge University Press
Page : 404 pages
File Size : 49,6 Mb
Release : 2024-05-31
Category : Mathematics
ISBN : 9781009546577
Research in recent years has highlighted the deep connections between the algebraic, geometric, and analytic structures of a discrete group. New methods and ideas have resulted in an exciting field, with many opportunities for new researchers. This book is an introduction to the area from a modern vantage point. It incorporates the main basics, such as Kesten's amenability criterion, Coulhon and Saloff-Coste inequality, random walk entropy and bounded harmonic functions, the Choquet–Deny Theorem, the Milnor–Wolf Theorem, and a complete proof of Gromov's Theorem on polynomial growth groups. The book is especially appropriate for young researchers, and those new to the field, accessible even to graduate students. An abundance of examples, exercises, and solutions encourage self-reflection and the internalization of the concepts introduced. The author also points to open problems and possibilities for further research.
Author : Gabriel P. Paternain,Mikko Salo,Gunther Uhlmann
Publisher : Cambridge University Press
Page : 370 pages
File Size : 46,5 Mb
Release : 2023-01-05
Category : Mathematics
ISBN : 9781009041423
This up-to-date treatment of recent developments in geometric inverse problems introduces graduate students and researchers to an exciting area of research. With an emphasis on the two-dimensional case, topics covered include geodesic X-ray transforms, boundary rigidity, tensor tomography, attenuated X-ray transforms and the Calderón problem. The presentation is self-contained and begins with the Radon transform and radial sound speeds as motivating examples. The required geometric background is developed in detail in the context of simple manifolds with boundary. An in-depth analysis of various geodesic X-ray transforms is carried out together with related uniqueness, stability, reconstruction and range characterization results. Highlights include a proof of boundary rigidity for simple surfaces as well as scattering rigidity for connections. The concluding chapter discusses current open problems and related topics. The numerous exercises and examples make this book an excellent self-study resource or text for a one-semester course or seminar.
Author : Guillermo Pineda Villavicencio
Publisher : Cambridge University Press
Page : 482 pages
File Size : 47,9 Mb
Release : 2024-02-29
Category : Mathematics
ISBN : 9781009257787
This book introduces convex polytopes and their graphs, alongside the results and methodologies required to study them. It guides the reader from the basics to current research, presenting many open problems to facilitate the transition. The book includes results not previously found in other books, such as: the edge connectivity and linkedness of graphs of polytopes; the characterisation of their cycle space; the Minkowski decomposition of polytopes from the perspective of geometric graphs; Lei Xue's recent lower bound theorem on the number of faces of polytopes with a small number of vertices; and Gil Kalai's rigidity proof of the lower bound theorem for simplicial polytopes. This accessible introduction covers prerequisites from linear algebra, graph theory, and polytope theory. Each chapter concludes with exercises of varying difficulty, designed to help the reader engage with new concepts. These features make the book ideal for students and researchers new to the field.
Author : Richard Stanley
Publisher : Cambridge University Press
Page : 801 pages
File Size : 49,8 Mb
Release : 2023-08-17
Category : Mathematics
ISBN : 9781009262491
Revised second volume of the standard guide to enumerative combinatorics, including the theory of symmetric functions and 159 new exercises.
Author : Robin Pemantle,Mark C. Wilson,Stephen Melczer
Publisher : Cambridge University Press
Page : 594 pages
File Size : 40,5 Mb
Release : 2024-02-15
Category : Mathematics
ISBN : 9781108877930
Discrete structures model a vast array of objects ranging from DNA sequences to internet networks. The theory of generating functions provides an algebraic framework for discrete structures to be enumerated using mathematical tools. This book is the result of 25 years of work developing analytic machinery to recover asymptotics of multivariate sequences from their generating functions, using multivariate methods that rely on a combination of analytic, algebraic, and topological tools. The resulting theory of analytic combinatorics in several variables is put to use in diverse applications from mathematics, combinatorics, computer science, and the natural sciences. This new edition is even more accessible to graduate students, with many more exercises, computational examples with Sage worksheets to illustrate the main results, updated background material, additional illustrations, and a new chapter providing a conceptual overview.
Author : Masayuki Kawakita
Publisher : Cambridge University Press
Page : 503 pages
File Size : 44,5 Mb
Release : 2023-11-30
Category : Mathematics
ISBN : 9781108844239
A detailed treatment of the explicit aspects of the birational geometry of algebraic threefolds arising from the minimal model program.
Author : Richard Stanley
Publisher : Cambridge University Press
Page : 802 pages
File Size : 45,7 Mb
Release : 2023-07-31
Category : Mathematics
ISBN : 9781009262514
Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of volume two covers the composition of generating functions, in particular the exponential formula and the Lagrange inversion formula, labelled and unlabelled trees, algebraic, D-finite, and noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course and focusing on combinatorics, especially the Robinson–Schensted–Knuth algorithm. An appendix by Sergey Fomin covers some deeper aspects of symmetric functions, including jeu de taquin and the Littlewood–Richardson rule. The exercises in the book play a vital role in developing the material, and this second edition features over 400 exercises, including 159 new exercises on symmetric functions, all with solutions or references to solutions.
Author : Yujiro Kawamata
Publisher : Cambridge University Press
Page : 263 pages
File Size : 48,5 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 9781009344678
The finite generation theorem is a major achievement of modern algebraic geometry. Based on the minimal model theory, it states that the canonical ring of an algebraic variety defined over a field of characteristic zero is a finitely generated graded ring. This graduate-level text is the first to explain this proof. It covers the progress on the minimal model theory over the last 30 years, culminating in the landmark paper on finite generation by Birkar-Cascini-Hacon-McKernan. Building up to this proof, the author presents important results and techniques that are now part of the standard toolbox of birational geometry, including Mori's bend and break method, vanishing theorems, positivity theorems and Siu's analysis on multiplier ideal sheaves. Assuming only the basics in algebraic geometry, the text keeps prerequisites to a minimum with self-contained explanations of terminology and theorems.