Download or read book Cremona Groups and the Icosahedron written by Ivan Cheltsov and published by CRC Press. This book was released on 2015-08-21 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cremona Groups and the Icosahedron focuses on the Cremona groups of ranks 2 and 3 and describes the beautiful appearances of the icosahedral group A5 in them. The book surveys known facts about surfaces with an action of A5, explores A5-equivariant geometry of the quintic del Pezzo threefold V5, and gives a proof of its A5-birational rigidity. The authors explicitly describe many interesting A5-invariant subvarieties of V5, including A5-orbits, low-degree curves, invariant anticanonical K3 surfaces, and a mildly singular surface of general type that is a degree five cover of the diagonal Clebsch cubic surface. They also present two birational selfmaps of V5 that commute with A5-action and use them to determine the whole group of A5-birational automorphisms. As a result of this study, they produce three non-conjugate icosahedral subgroups in the Cremona group of rank 3, one of them arising from the threefold V5. This book presents up-to-date tools for studying birational geometry of higher-dimensional varieties. In particular, it provides readers with a deep understanding of the biregular and birational geometry of V5.
Download or read book The Cremona Group and Its Subgroups written by Julie Déserti and published by American Mathematical Soc.. This book was released on 2021-04-13 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to present a portrait of the n n-dimensional Cremona group with an emphasis on the 2-dimensional case. After recalling some crucial tools, the book describes a naturally defined infinite dimensional hyperbolic space on which the Cremona group acts. This space plays a fundamental role in the study of Cremona groups, as it allows one to apply tools from geometric group theory to explore properties of the subgroups of the Cremona group as well as the degree growth and dynamical behavior of birational transformations. The book describes natural topologies on the Cremona group, codifies the notion of algebraic subgroups of the Cremona groups and finishes with a chapter on the dynamics of their actions. This book is aimed at graduate students and researchers in algebraic geometry who are interested in birational geometry and its interactions with geometric group theory and dynamical systems.
Download or read book Algebraic Geometry Salt Lake City 2015 Part 1 written by Tommaso de Fernex and published by American Mathematical Soc.. This book was released on 2018-06-01 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is Part 1 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic and -adic tools, etc. The resulting articles will be important references in these areas for years to come.
Download or read book The Calabi Problem for Fano Threefolds written by Carolina Araujo and published by Cambridge University Press. This book was released on 2023-06-30 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book determines whether the general element of each family of Fano threefolds is K-polystable, a major problem in mathematics.
Download or read book Computation with Linear Algebraic Groups written by Willem Adriaan de Graaf and published by CRC Press. This book was released on 2017-08-07 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed as a self-contained account of a number of key algorithmic problems and their solutions for linear algebraic groups, this book combines in one single text both an introduction to the basic theory of linear algebraic groups and a substantial collection of useful algorithms. Computation with Linear Algebraic Groups offers an invaluable guide to graduate students and researchers working in algebraic groups, computational algebraic geometry, and computational group theory, as well as those looking for a concise introduction to the theory of linear algebraic groups.
Download or read book Actions and Invariants of Algebraic Groups written by Walter Ricardo Ferrer Santos and published by CRC Press. This book was released on 2017-09-19 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Actions and Invariants of Algebraic Groups, Second Edition presents a self-contained introduction to geometric invariant theory starting from the basic theory of affine algebraic groups and proceeding towards more sophisticated dimensions." Building on the first edition, this book provides an introduction to the theory by equipping the reader with the tools needed to read advanced research in the field. Beginning with commutative algebra, algebraic geometry and the theory of Lie algebras, the book develops the necessary background of affine algebraic groups over an algebraically closed field, and then moves toward the algebraic and geometric aspects of modern invariant theory and quotients.
Download or read book Diagram Genus Generators and Applications written by Alexander Stoimenow and published by CRC Press. This book was released on 2018-09-03 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: In knot theory, diagrams of a given canonical genus can be described by means of a finite number of patterns ("generators"). Diagram Genus, Generators and Applications presents a self-contained account of the canonical genus: the genus of knot diagrams. The author explores recent research on the combinatorial theory of knots and supplies proofs for a number of theorems. The book begins with an introduction to the origin of knot tables and the background details, including diagrams, surfaces, and invariants. It then derives a new description of generators using Hirasawa’s algorithm and extends this description to push the compilation of knot generators one genus further to complete their classification for genus 4. Subsequent chapters cover applications of the genus 4 classification, including the braid index, polynomial invariants, hyperbolic volume, and Vassiliev invariants. The final chapter presents further research related to generators, which helps readers see applications of generators in a broader context.
Download or read book Modeling and Inverse Problems in the Presence of Uncertainty written by H. T. Banks and published by CRC Press. This book was released on 2014-04-01 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling and Inverse Problems in the Presence of Uncertainty collects recent research—including the authors’ own substantial projects—on uncertainty propagation and quantification. It covers two sources of uncertainty: where uncertainty is present primarily due to measurement errors and where uncertainty is present due to the modeling formulation itself. After a useful review of relevant probability and statistical concepts, the book summarizes mathematical and statistical aspects of inverse problem methodology, including ordinary, weighted, and generalized least-squares formulations. It then discusses asymptotic theories, bootstrapping, and issues related to the evaluation of correctness of assumed form of statistical models. The authors go on to present methods for evaluating and comparing the validity of appropriateness of a collection of models for describing a given data set, including statistically based model selection and comparison techniques. They also explore recent results on the estimation of probability distributions when they are embedded in complex mathematical models and only aggregate (not individual) data are available. In addition, they briefly discuss the optimal design of experiments in support of inverse problems for given models. The book concludes with a focus on uncertainty in model formulation itself, covering the general relationship of differential equations driven by white noise and the ones driven by colored noise in terms of their resulting probability density functions. It also deals with questions related to the appropriateness of discrete versus continuum models in transitions from small to large numbers of individuals. With many examples throughout addressing problems in physics, biology, and other areas, this book is intended for applied mathematicians interested in deterministic and/or stochastic models and their interactions. It is also suitable for scientists in biology, medicine, engineering, and physics working on basic modeling and inverse problems, uncertainty in modeling, propagation of uncertainty, and statistical modeling.
Download or read book Signal Processing written by Charles L. Byrne and published by CRC Press. This book was released on 2014-11-12 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Signal Processing: A Mathematical Approach is designed to show how many of the mathematical tools the reader knows can be used to understand and employ signal processing techniques in an applied environment. Assuming an advanced undergraduate- or graduate-level understanding of mathematics-including familiarity with Fourier series, matrices, probab
Download or read book Monomial Algebras written by Rafael Villarreal and published by CRC Press. This book was released on 2018-10-08 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monomial Algebras, Second Edition presents algebraic, combinatorial, and computational methods for studying monomial algebras and their ideals, including Stanley–Reisner rings, monomial subrings, Ehrhart rings, and blowup algebras. It emphasizes square-free monomials and the corresponding graphs, clutters, or hypergraphs. New to the Second Edition Four new chapters that focus on the algebraic properties of blowup algebras in combinatorial optimization problems of clutters and hypergraphs Two new chapters that explore the algebraic and combinatorial properties of the edge ideal of clutters and hypergraphs Full revisions of existing chapters to provide an up-to-date account of the subject Bringing together several areas of pure and applied mathematics, this book shows how monomial algebras are related to polyhedral geometry, combinatorial optimization, and combinatorics of hypergraphs. It directly links the algebraic properties of monomial algebras to combinatorial structures (such as simplicial complexes, posets, digraphs, graphs, and clutters) and linear optimization problems.
Download or read book Special Integrals of Gradshteyn and Ryzhik written by Victor H. Moll and published by CRC Press. This book was released on 2015-10-27 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Guide to the Evaluation of Integrals Special Integrals of Gradshetyn and Ryzhik: the Proofs provides self-contained proofs of a variety of entries in the frequently used table of integrals by I.S. Gradshteyn and I.M. Ryzhik. The book gives the most elementary arguments possible and uses Mathematica® to verify the formulas. You will discover the beauty, patterns, and unexpected connections behind the formulas. Volume II collects 14 papers from Revista Scientia covering elliptic integrals, the Riemann zeta function, the error function, hypergeometric and hyperbolic functions, Bessel-K functions, logarithms and rational functions, polylogarithm functions, the exponential integral, and Whittaker functions. Many entries have a variety of proofs that can be evaluated using a symbolic language or point to the development of a new algorithm.
Download or read book Noncommutative Deformation Theory written by Eivind Eriksen and published by CRC Press. This book was released on 2017-09-19 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative Deformation Theory is aimed at mathematicians and physicists studying the local structure of moduli spaces in algebraic geometry. This book introduces a general theory of noncommutative deformations, with applications to the study of moduli spaces of representations of associative algebras and to quantum theory in physics. An essential part of this theory is the study of obstructions of liftings of representations using generalised (matric) Massey products. Suitable for researchers in algebraic geometry and mathematical physics interested in the workings of noncommutative algebraic geometry, it may also be useful for advanced graduate students in these fields.
Download or read book Mathematical Modelling of Waves in Multi Scale Structured Media written by Alexander B. Movchan and published by CRC Press. This book was released on 2017-11-09 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Modelling of Waves in Multi-Scale Structured Media presents novel analytical and numerical models of waves in structured elastic media, with emphasis on the asymptotic analysis of phenomena such as dynamic anisotropy, localisation, filtering and polarisation as well as on the modelling of photonic, phononic, and platonic crystals.
Download or read book Partial Differential Equations with Variable Exponents written by Vicentiu D. Radulescu and published by CRC Press. This book was released on 2015-06-24 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type. The book presents the most important variational
Download or read book Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications written by Daniele Bertaccini and published by CRC Press. This book was released on 2018-02-19 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear systems. The solution of large and sparse linear systems is the most time-consuming part for most of the scientific computing simulations. Indeed, mathematical models become more and more accurate by including a greater volume of data, but this requires the solution of larger and harder algebraic systems. In recent years, research has focused on the efficient solution of large sparse and/or structured systems generated by the discretization of numerical models by using iterative solvers.
Download or read book Blow up for Higher Order Parabolic Hyperbolic Dispersion and Schrodinger Equations written by Victor A. Galaktionov and published by CRC Press. This book was released on 2014-09-22 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations. The authors present a unified approach to deal with these quasilinear PDEs.The book
Download or read book Nonlinear Reaction Diffusion Convection Equations written by Roman Cherniha and published by CRC Press. This book was released on 2017-11-02 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that symmetry-based methods are very powerful tools for investigating nonlinear partial differential equations (PDEs), notably for their reduction to those of lower dimensionality (e.g. to ODEs) and constructing exact solutions. This book is devoted to (1) search Lie and conditional (non-classical) symmetries of nonlinear RDC equations, (2) constructing exact solutions using the symmetries obtained, and (3) their applications for solving some biologically and physically motivated problems. The book summarises the results derived by the authors during the last 10 years and those obtained by some other authors.
