Character Theory And The Mckay Conjecture
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Character Theory And The Mckay Conjecture
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Author : Gabriel Navarro
language : en
Publisher: Cambridge University Press
Release Date : 2018-04-26
Character Theory And The Mckay Conjecture written by Gabriel Navarro and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-26 with Mathematics categories.
Presents contemporary character theory of finite groups from the basics to the state of the art, with new, refined proofs.
Harmonic Functions And Random Walks On Groups
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Author : Ariel Yadin
language : en
Publisher: Cambridge University Press
Release Date : 2024-05-31
Harmonic Functions And Random Walks On Groups written by Ariel Yadin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-31 with Mathematics categories.
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.
Equivariant Cohomology In Algebraic Geometry
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Author : David Anderson
language : en
Publisher: Cambridge University Press
Release Date : 2023-10-26
Equivariant Cohomology In Algebraic Geometry written by David Anderson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-26 with Mathematics categories.
Equivariant cohomology has become an indispensable tool in algebraic geometry and in related areas including representation theory, combinatorial and enumerative geometry, and algebraic combinatorics. This text introduces the main ideas of the subject for first- or second-year graduate students in mathematics, as well as researchers working in algebraic geometry or combinatorics. The first six chapters cover the basics: definitions via finite-dimensional approximation spaces, computations in projective space, and the localization theorem. The rest of the text focuses on examples – toric varieties, Grassmannians, and homogeneous spaces – along with applications to Schubert calculus and degeneracy loci. Prerequisites are kept to a minimum, so that one-semester graduate-level courses in algebraic geometry and topology should be sufficient preparation. Featuring numerous exercises, examples, and material that has not previously appeared in textbook form, this book will be a must-have reference and resource for both students and researchers for years to come.
Geometric Inverse Problems
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Author : Gabriel P. Paternain
language : en
Publisher: Cambridge University Press
Release Date : 2023-01-05
Geometric Inverse Problems written by Gabriel P. Paternain and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-05 with Mathematics categories.
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.
Analytic Combinatorics In Several Variables
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Author : Robin Pemantle
language : en
Publisher: Cambridge University Press
Release Date : 2024-02-15
Analytic Combinatorics In Several Variables written by Robin Pemantle and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-15 with Mathematics categories.
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.
Complex Algebraic Threefolds
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Author : Masayuki Kawakita
language : en
Publisher: Cambridge University Press
Release Date : 2023-10-19
Complex Algebraic Threefolds written by Masayuki Kawakita and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-19 with Mathematics categories.
A detailed treatment of the explicit aspects of the birational geometry of algebraic threefolds arising from the minimal model program.
Algebraic Varieties Minimal Models And Finite Generation
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Author : Yujiro Kawamata
language : en
Publisher: Cambridge University Press
Release Date : 2024-06-30
Algebraic Varieties Minimal Models And Finite Generation written by Yujiro Kawamata and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-30 with Mathematics categories.
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.
Enumerative Combinatorics
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Author : Richard Stanley
language : en
Publisher: Cambridge University Press
Release Date : 2023-08-17
Enumerative Combinatorics written by Richard Stanley and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-17 with Mathematics categories.
Revised second volume of the standard guide to enumerative combinatorics, including the theory of symmetric functions and 159 new exercises.
Polytopes And Graphs
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Author : Guillermo Pineda Villavicencio
language : en
Publisher: Cambridge University Press
Release Date : 2024-02-29
Polytopes And Graphs written by Guillermo Pineda Villavicencio and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-29 with Mathematics categories.
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.
The Character Theory Of Finite Groups Of Lie Type
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Author : Meinolf Geck
language : en
Publisher: Cambridge University Press
Release Date : 2020-02-27
The Character Theory Of Finite Groups Of Lie Type written by Meinolf Geck and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-27 with Mathematics categories.
A comprehensive guide to the vast literature and range of results around Lusztig's character theory of finite groups of Lie type.