Algebraic geometry Books

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Book SynopsisThis two-volume set focuses on linear algebra for graduate students in mathematics, the sciences, and economics. Proofs are emphasized and the overall objective is to understand the structure of linear operators as the key to solving problems in which they arise.Table of Contents Part : Vector Spaces Over a Field $\mathbb{K}$ Linear Operators $T: V \to W$ Duality and the Dual Space $V^*$ Determinants The Diagonalization Problem Inner Product Spaces Index Part : Generalized Eigenspaces and the Jordon Decomposition Further Applications of Jordon Form Bilinear, Quadratic, and Multilinear Forms Tensor Fields, Manifolds, and Vector Calculus Matrix Lie Groups Bibliography.

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Book SynopsisProvides an elementary analytically inclined journey to a fundamental result of linear algebra: the Singular Value Decomposition (SVD). SVD is a workhorse in many applications of linear algebra to data science. Four important applications relevant to data science are considered throughout the book.Table of Contents Introduction Linear algebra and normed vector spaces Main tools The spectral theorem The singular value decomposition Applications revisited A glimpse towards infinite dimensions Bibliography Index of notation Index

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Book SynopsisProvides a broad introduction to perfectoid spaces. The book will be an invaluable asset for any graduate student or researcher interested in the theory of perfectoid spaces and their applications.Table of Contents J. Weinstein, Arizona Winter School 2017: Adic spaces K. S. Kedlaya, Sheaves, stacks, and shtukas B. Bhatt, The Hodge-Tate decomposition via perfectoid spaces A. Caraiani, Perfectoid Shimura varieties

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Book SynopsisWe develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms, cohomology spaces and spaces of eigenfunctions of transfer operators.

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Book SynopsisProvides an introduction to an active area of research that lies at the intersection of number theory, $p$-adic analysis, algebraic geometry, singularity theory, and theoretical physics. The book introduces $p$-adic analysis, the theory of zeta functions, Archimedean, $p$-adic, motivic, singularities of plane curves and their Poincare series.Table of Contents Surveys: E. Leon-Cardenal, Archimedean zeta functions and oscillatory integrals J. J. Moyano-Fernandez, Generalized Poincare series for plane curve singularities N. Potemans and W. Veys, Introduction to $p$-adic Igusa zeta functions J. Viu-Sos, An introduction to $p$-adic and motivic integration, zeta functions and invariants of singularities W. A. Zuniga-Galindo, $p$-adic analysis: A quick introduction Articles: E. Artal Bartolo and M. Gonzalez Villa, On maximal order poles of generalized topological zeta functions J. I. Cogolludo-Agustin, T. Laszlo, J. Martin-Morales, and A. Nemethi, Local invariants of minimal generic curves on rational surfaces J. Nagy and A. Nemethi, Motivic Poincare series of cusp surface singularities C. D. Sinclair, Non-Archimedean electrostatics

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Book SynopsisThe second of a three-volume set of books on the theory of algebras, a study that provides a consistent framework for understanding algebraic systems, including groups, rings, modules, semigroups and lattices.Table of Contents The classification of varieties Equational logic Rudiments of model theory Bibliography Index

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Book SynopsisThe third of a three-volume set of books on the theory of algebras, a study that provides a consistent framework for understanding algebraic systems, including groups, rings, modules, semigroups and lattices.Table of Contents Finite algebras and their clones Abstract clone theory Commutator theory Bibliography Index

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Book SynopsisContains the proceedings of the Virtual Conference on Noncommutative Rings and their Applications VII, held in July 2021, and the Virtual Conference on Quadratic Forms, Rings and Codes, held in July 2021. The articles cover topics in commutative and noncommutative algebra and applications to coding theory.Table of Contents R. R. de Araujo, A. L. M. Pereira, and C. Polcino Milies, A note on checkable codes over Frobenius and quasi-Frobenius rings N. Aydin, T. Guidotti, and P. Liu, Good classical and quantum codes from multi-twisted codes N. Bennenni and A. Leroy, Evaluation of iterated ore polynomials and skew Reed-Muller codes G. Blachar, L. H Rowen, and U. Vishne, Identities of the algebra $\mathbb{O}\otimes\mathbb{O}$ S. Breaz and Y. Zhou, When is every non central-unit a sum of two nilpotents? A. Chapman and K. McKinnie, Asymptotic Brauer $p$-dimension L. W. Christensen, S. Estrada, and P. Thompson, Five theorems on Gorenstein global dimensions S. T. Dougherty and S. Sahinkaya, Quasi-self-dual codes over a non-unital ring of order 4 S. T. Dougherty, S. Sahinkaya, and D. Ustun, Codes from the skew ring $M_2(\mathbb{F}_2\rtimes_\varphi G$ F. D'Este, The underlying vector spaces of certain endomorhism rings A. Facchini, Algebraic structures from the point of view of complete multiplicative lattices C. Fernandez-Cordoba and S. Szabo, $\mathbb{Z}_2\mathbb{Z}_4$-additive codes as codes over rings G. Lee, C. S. Roman, N. K. Tung, and X. Zhang, On Utumi rings and continuous regular Baer rings S. K. Jain and A. Leroy, Matrices representable as product of conjugates of a singular matrix F. Kaynarca, G. D'Este, and D. Keskin Tutuncu, Almost projective modules over non-hereditary algebras M. Salahuddin Khan, A. Abbasi, S. Ali, and M. Ayedh, On prime ideals with generalized derivations in rings with involution J. Krempa, On nil algebras and a problem of Passeman concerning nilpotent free algebras X. Mary, Rings with transitive chaining of idempotents J. K. Park and S. T. Rizvi, On continuous hulls of rings and modules

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Book SynopsisOffers a new approach to laying a foundation for abstract mathematics. Prior experience with proofs is not assumed, and the book takes time to build proof-writing skills in ways that will serve students through a lifetime of learning and creating mathematics.Table of Contents Preliminaries: Introduction to proofs Sets and subsets Divisors Examples of groups: Modular arithmetic Symmetries Permutations Matrices Introduction to groups: Introduction to groups Groups of small size Matrix groups Subgroups Order of an element Cyclic groups, Part I Cyclic groups, Part II Group homomorphisms: Functions Isomorphisms Homomorphisms, Part I Homomorphisms, Part II Quotient groups: Introduction to cosets Lagrange's theorem Multiplying/adding cosets Quotient group examples Quotient group proofs Normal subgroups First isomorphism theorem Introduction to rings: Introduction to rings Integral domains and fields Polynomial rings, Part I Polynomial rings, Part II Factoring polynomials Quotient rings: Ring homomorphisms Introduction to quotient rings Quotient ring $\mathbb{Z}_7[x]/ \langle x^2-1\rangle$ Quotient ring $\mathbb{R}[x]/ \langle x^2 +1\rangle$ $F[x]/ \langle g(x)\rangle$ is/isn't a field, Part I Maximal ideals $F[x]/ \langle g(x)\rangle$ is/isn't a field, Part II Appendices: Proof of the GCD theorem Composition table for $D_4$ Symbols and notations Essential theorems Index: Index of terms

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Book SynopsisPresents survey articles providing a user-friendly introduction to applications of cyclic cohomology in such areas as higher categorical algebra, Hopf algebra symmetries, de Rham-Witt complex, quantum physics, etc, in which cyclic homology plays the role of a unifying theme.Table of Contents A. Baldare, M. Benameur, and V. Nistor, Chern-Connes-Karoubi character isomorphisms and algebras of symbols of pseudodifferential operators J. Block, N. Higson, and J. Sanchez Jr., On Perrot's index cocycles P. Carrillo Rouse, The Chern-Baum Connes assembly map for Lie groupoids A. Connes and C. Consani, Hochschild homology, trace map and $\zeta$-cycles A. Connes and C. Consani, Cyclic theory and the pericyclic category J. Cuntz, The image of Bott peridocity in cyclic homology B. I. Dundas, Applications of topological cyclic homology to algebraic $K$-theory D. Gepner, Algebraic $K$-theory and generalized stable homotopy theory A. Gorokhovsky and E. van Erp, Cyclic cohomology and the extended Heisenberg calculus of Epstein and Melrose L. Hesselholt, Topological cyclic homology and the Fargues-Fontaine curve M. Khalkhali and I. Shapiro, Hopf cyclic cohomology and beyond M. Lorentz, The Hochschild cohomology of uniform Roe algebras E. McDonald, F. Sukochev, and X. Xiong, Quantum differntiability-The analytical perspective R. Meyer and D. Mukherjee, Local cyclic homology for nonarchimedean Banach algebras H. Moscovici, On the van Est analogy in Hopf cyclic cohomology P. Piazza and X. Tang, Primary and secondary invariants of Dirac operators on $G$-proper manifolds M. J. Pflaum, Localization in Hochschild homology R. Ponge, Cyclic homology and group actions E. Prodan, Cyclic cocycles and quantized pairings in materials science M. Puschnigg, Periodic cyclic homology of crossed products A. Savin and E. Schrohe, Trace expansions and equivariant traces on an algebra of Fourier integral operators on $\mathbb{R}^n$ Y. Song and X. Tang, Carton motion group and orbital integrals B. Tsygan, On noncommutative crystalline cohomology T. D. H. Van Nuland and W. D. van Suijlekom, Cyclic cocycles and one-loop corrections in the spectral action J. Wang, Z. Xie, and G. Yu, $\ell^1$-higher index, $\ell^1$-higher rho invariant and cyclic cohomology.

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Book SynopsisLinear algebra permeates mathematics, as well as physics and engineering. In this text for junior and senior undergraduates, Sadun treats diagonalization as a central tool in solving complicated problems in these subjects by reducing coupled linear evolution problems to a sequence of simpler decoupled problems. This is the Decoupling Principle. Traditionally, difference equations, Markov chains, coupled oscillators, Fourier series, the wave equation, the Schroedinger equation, and Fourier transforms are treated separately, often in different courses. Here, they are treated as particular instances of the decoupling principle, and their solutions are remarkably similar. By understanding this general principle and the many applications given in the book, students will be able to recognize it and to apply it in many other settings. Sadun includes some topics relating to infinite-dimensional spaces. He does not present a general theory, but enough so as to apply the decoupling principle to

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Book SynopsisDevelops the machinery of homological algebra and its applications to commutative rings and modules. The book assumes familiarity with basic commutative algebra. This is a valuable resource for anyone interested in learning about homological algebra and its applications in commutative algebra.Table of Contents Categories Abelian categories Derived functors Spectral sequences Projective and injective modules Flatness Koszul complexes and regular sequences Regularity Mild singularities Local cohomology and duality Background material Bibliography Index of notation Index

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Book SynopsisPresents a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade.Table of Contents Prerequisites Dimension and rank Gaussian elimination Eigenvalues and eigenvectors Towards the Jordan decomposition The Jordan decomposition Determinants Companion matrices and circulants Inequalities Normed linear spaces Inner product spaces Orthogonality Normal matrices Projections, volumes, and traces Singular value decomposition Positive definite and semidefinite matrices Determinants redux Applications Discrete dynamical systems Continuous dynamical systems Vector-valued functions Fixed point theorems The implicit function theorem Extremal problems Newton's method Matrices with nonnegative entries Applications of matrices with nonnegative entries Eigenvalues of Hermitian matrices Singular values redux I Singular values redux II Approximation by unitary matrices Linear functionals A minimal norm problem Conjugate gradients Continuity of eigenvalues Eigenvalue location problems Matrix equations A matrix completion problem Minimal norm completions The numerical range Riccati equations Supplementary topics Toeplitz, Hankel, and de Branges Bibliography Notation index Subject index.

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Book SynopsisWith numerical, graphical, and theoretical methods, this book examines the relevance of mathematical models to phenomena ranging from population growth and economics to medicine and the physical sciences.Trade ReviewKalman uses basic growth models...not only to convey the power of mathematics in solving real-world problems, but also to motivate the study of the elementary functions usually encountered in college algebra courses. There is a natural evolution from a simple hypotheses to difference equations, to their solutions, to the study of the elementary functions associated with the solutions. There is an emphasis on the ""why"" of algebra and on manipulation associated with applications rather than for its own sake.Numerical, graphical, and symbolic approaches are used throughout, and the numerous exercises include reading comprehension exercises and group selected exercises...Aimed at students at the college algebra or liberals arts mathematics level, the slow careful development should be clear even to those with a weak algebraic background. Highly recommended."" - Choice""An innovative alternative to introductory college mathematics intended for any student not headed for calculus. Uses discrete and continuous models of growth to introduce increasingly sophisticated algebraic patterns...An effective blend of narrative, motivation, calculation, and graphical representation that introduces algebraic thinking with a minimum of algebraic formalisms."" - The American Mathematical Monthly""The book is well balanced and succeeds in introducing the use of discrete models to students who might view a mathematics class with a weary eye...the author does a superb job of addressing a difficult audience. This is especially true of the problem sets. An excellent mix of reading, simple/short answer, and word problems of varying difficulties are given. Furthermore, complete answers to some of the problems are given in the same chapter, rather than in an appendix."" - Kelly Black, University of New Hampshire""This book can be described as the protocol of the ultimate (and apparently successful) teaching experiment, namely to lead students with hardly any mathematical background at all, to a respectable level in the fundamentals of mathematics in such a way, that they will always have positive thoughts about it. ...The expert reader may use this book as a rich source of growth problems."" - Springer-Verlag, Zentallblatt fur Mathematik""I found the book a refreshing alternative to college algebra textbooks and would recommend it to instructors who are seeking changes."" - The Mathematics Teacher

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Book SynopsisPresents a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade.Table of Contents Prerequisites Dimension and rank Gaussian elimination Eigenvalues and eigenvectors Towards the Jordan decomposition The Jordan decomposition Determinants Companion matrices and circulants Inequalities Normed linear spaces Inner product spaces Orthogonality Normal matrices Projections, volumes, and traces Singular value decomposition Positive definite and semidefinite matrices Determinants redux Applications Discrete dynamical systems Continuous dynamical systems Vector-valued functions Fixed point theorems The implicit function theorem Extremal problems Newton's method Matrices with nonnegative entries Applications of matrices with nonnegative entries Eigenvalues of Hermitian matrices Singular values redux I Singular values redux II Approximation by unitary matrices Linear functionals A minimal norm problem Conjugate gradients Continuity of eigenvalues Eigenvalue location problems Matrix equations A matrix completion problem Minimal norm completions The numerical range Riccati equations Supplementary topics Toeplitz, Hankel, and de Branges Bibliography Notation index Subject index.

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Book SynopsisDevelops the machinery of homological algebra and its applications to commutative rings and modules. The book assumes familiarity with basic commutative algebra. This is a valuable resource for anyone interested in learning about homological algebra and its applications in commutative algebra.Table of Contents Categories Abelian categories Derived functors Spectral sequences Projective and injective modules Flatness Koszul complexes and regular sequences Regularity Mild singularities Local cohomology and duality Background material Bibliography Index of notation Index

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Book SynopsisThe tenth in a series of volumes whose aim is to provide a complete proof of the classification theorem for the finite simple groups based on a fairly short and clearly enumerated set of background results. This book completes our identification of the simple groups of bicharacteristic type begun in the ninth volume of the series.Table of Contents General group-theoretic lemmas Theorem $\mathscr{C}_6$ and $\mathscr{C}_6^*$ Theorems $\mathscr{C}_4$ and $\mathscr{C}_4^*$: Introduction Theorem $\mathscr{C}_4^*$: Stage A1. First steps Theorem $\mathscr{C}_4^*$: Stage A2. Nonconstrained $p$-rank 3 centralizers Theorem $\mathscr{C}_4^*$: Stage A3. $KM$-singularities Theorem $\mathscr{C}_4^*$: Stage A4. Setups for recognizing $G$ Theorem $\mathscr{C}_4^*$: Stage A5. Recognition Properties of $\mathscr{K}$-groups Bibliography Index

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Book SynopsisWhenever two or more objects or entities—be they bubbles, vortices, black holes, magnets, colloidal particles, microorganisms, swimming bacteria, Brownian random walkers, airfoils, turbine blades, electrified drops, magnetized particles, dislocations, cracks, or heterogeneities in an elastic solid—interact in some ambient medium, they make holes in that medium. Such holey regions with interacting entities are called multiply connected.This book describes a novel mathematical framework for solving problems in two-dimensional, multiply connected regions. The framework is built on a central theoretical concept: the prime function, whose significance for the applied sciences, especially for solving problems in multiply connected domains, has been missed until recent work by the author.This monograph is a one-of-a-kind treatise on the prime function associated with multiply connected domains and how to use it in applications. The book contains many results familiar in the simply connected, or single-entity, case that are generalized naturally to any number of entities, in many instances for the first time.Solving Problems in Multiply Connected Domains is aimed at applied and pure mathematicians, engineers, physicists, and other natural scientists; the framework it describes finds application in a diverse array of contexts. The book provides a rich source of project material for undergraduate and graduate courses in the applied sciences and could serve as a complement to standard texts on advanced calculus, potential theory, partial differential equations and complex analysis, and as a supplement to texts on applied mathematical methods in engineering and science.

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Book SynopsisMuch of modern algebra arose from attempts to prove Fermat's Last Theorem, which in turn has its roots in Diophantus' classification of Pythagorean triples. This book, designed for prospective and practising mathematics teachers, makes explicit connections between the ideas of abstract algebra and the mathematics taught at high-school level. Algebraic concepts are presented in historical order, and the book also demonstrates how other important themes in algebra arose from questions related to teaching. The focus is on number theory, polynomials, and commutative rings. Group theory is introduced near the end of the text to explain why generalisations of the quadratic formula do not exist for polynomials of high degree, allowing the reader to appreciate the work of Galois and Abel. Results are motivated with specific examples, and applications range from the theory of repeating decimals to the use of imaginary quadratic fields to construct problems with rational solutions.Trade ReviewThis book covers abstract algebra from a historical perspective by using mathematics from attempts to prove Fermat's last theorem, as the title indicates. The target audience is high school mathematics teachers. However, typical undergraduate students will also derive great benefit by studying this text. The book is permeated with fascinating mathematical nuggets that are clearly explained." - D. P. Turner, CHOICE"This book is destined for college students in the U.S. who intend to teach mathematics in high school. The reviewer finds it even more apt as a text for algebra courses. Special features in the book are side notes given and printed prominently at the margins of the pages, like: How to think about it, Historical notes, Etymology of notions and words. … The reviewer considers the book a refreshing read among the vast amount of books dealing with similar topics." - Robert W. van der Waall, Zentrallblatt MATH"Although this book is designed for college students who want to teach in high school," its mathematical richness fits it admirably as a text for a first abstract algebra course or a handbook for assiduous students working on their own. While definitions, examples, theorems and their proofs are organized formally, the book is enhanced by substantial historical notes, advice on "how to think about it," marginal comments, connections and etymology that are designed to "balance experience and formality." The book is tightly organized with the goal of elucidating developments leading to the solution of the Fermat conjecture and the theory of solvability by radicals." - E. J. Barbeau, Mathematical Reviews"The primary intended audience of the book is future high school teachers. The authors take great pains to relate the material covered here to subjects that are taught in high school mathematics classes. … In writing this book, the authors have obviously kept the needs of the student reader firmly in mind at all times. The writing style is not just clear; iit is often conversational and humorous. … There are lots of exercises covering a wide range of difficulty, some with hints (but none with complete solutions) and there is a pretty good 39-entry bibliography. … What might be a very interesting use for this book would be as a text for a senior seminar or “topics” course for students who already have some prior exposure to abstract algebra. And, of course, whatever may be the applicability of this book as a text for undergraduate course, it seems clear to me that it belongs in any good undergraduate library." - Mark Hunacek, MAA ReviewsTable of ContentsPreface; Some features of this book; A note to students; A note to instructors; Notation; 1. Early number theory; 2. Induction; 3. Renaissance; 4. Modular arithmetic; 5. Abstract algebra; 6. Arithmetic of polynomials; 7. Quotients, fields, and classical problems; 8. Cyclotomic integers; 9. Epilogue; References; Index.

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Book SynopsisThis monograph provides a systematic treatment of the Brauer group of schemes, from the foundational work of Grothendieck to recent applications in arithmetic and algebraic geometry. The importance of the cohomological Brauer group for applications to Diophantine equations and algebraic geometry was discovered soon after this group was introduced by Grothendieck. The Brauer–Manin obstruction plays a crucial role in the study of rational points on varieties over global fields. The birational invariance of the Brauer group was recently used in a novel way to establish the irrationality of many new classes of algebraic varieties. The book covers the vast theory underpinning these and other applications. Intended as an introduction to cohomological methods in algebraic geometry, most of the book is accessible to readers with a knowledge of algebra, algebraic geometry and algebraic number theory at graduate level. Much of the more advanced material is not readily available in book form elsewhere; notably, de Jong’s proof of Gabber’s theorem, the specialisation method and applications of the Brauer group to rationality questions, an in-depth study of the Brauer–Manin obstruction, and proof of the finiteness theorem for the Brauer group of abelian varieties and K3 surfaces over finitely generated fields. The book surveys recent work but also gives detailed proofs of basic theorems, maintaining a balance between general theory and concrete examples. Over half a century after Grothendieck's foundational seminars on the topic, The Brauer–Grothendieck Group is a treatise that fills a longstanding gap in the literature, providing researchers, including research students, with a valuable reference on a central object of algebraic and arithmetic geometry.Trade Review“The book gives a comprehensive, clear, up-to date presentation of the theory, including most proofs. A particular strength is that it nicely collects many results, examples and counterexamples from various areas of algebraic and arithmetic geometry … . the book fills a wide gap and is a most welcome addition to the literature.” (Stefan Schröer, zbMATH 1490.14001, 2022)“This book has collected in one place much of the fundamental cohomological theory of the Brauer group, along with excellent references. It then gives some coverage of further results, especially on the two important topics of obstructions to rationality and obstructions to the Hasse principle. For whatever is not included in this book, it gives a thorough and coherent overview of the relevant literature. Approximately four hundred references are given.” (Thomas Benedict Williams, Mathematical Reviews, September, 2022)Table of Contents1 Galois Cohomology.- 2 Étale Cohomology.- 3 Brauer Groups of Schemes.- 4 Comparison of the Two Brauer Groups, II.- 5 Varieties Over a Field.- 6 Birational Invariance.- 7 Severi–Brauer Varieties and Hypersurfaces.- 8 Singular Schemes and Varieties.- 9 Varieties with a Group Action.- 10 Schemes Over Local Rings and Fields.- 11 Families of Varieties.- 12 Rationality in a Family.- 13 The Brauer–Manin Set and the Formal Lemma.- 14 Are Rational Points Dense in the Brauer–Manin Set?.- 15 The Brauer–Manin Obstruction for Zero-Cycles.- 16 Tate Conjecture, Abelian Varieties and K3 Surfaces.- Bibliography.- Index.

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Book SynopsisThis volume contains articles related to the work of the Simons Collaboration “Arithmetic Geometry, Number Theory, and Computation.” The papers present mathematical results and algorithms necessary for the development of large-scale databases like the L-functions and Modular Forms Database (LMFDB). The authors aim to develop systematic tools for analyzing Diophantine properties of curves, surfaces, and abelian varieties over number fields and finite fields. The articles also explore examples important for future research.Specific topics include● algebraic varieties over finite fields● the Chabauty-Coleman method● modular forms● rational points on curves of small genus● S-unit equations and integral points.Table of Contents A robust implementation for solving the S-unit equation and several application (C. Rasmussen).- Computing classical modular forms for arbitrary congruence subgroups (E. Assaf).- Square root time Coleman integration on superelliptic curves (A. Best).- Computing classical modular forms ( A. Sutherland).- Elliptic curves with good reduction outside of the first six primes (B. Matschke).- Efficient computation of BSD invariants in genus 2 (R. van Bommel).- Restrictions on Weil polynomials of Jacobians of hyperelliptic curves (E. Costa).- Zen and the art of database maintenance (D. Roe).- Effective obstructions to lifting Tate classes from positive characteristic (E. Costa).- Conjecture: 100% of elliptic surfaces over Q have rank zero (A. Cowan).- On rational Bianchi newforms and abelian surfaces with quaternionic multiplication (J. Voight).- A database of Hilbert modular forms (J. Voight).- Isogeny classes of Abelian Varieties over Finite Fields in the LMFDB (D. Roe).- Computing rational points on genus 3 hyperelliptic curves (S. Hashimoto).- Curves with sharp Chabauty-Coleman bound (S. Gajović).- Chabauty-Coleman computations on rank 1 Picard curves (S. Hashimoto).- Linear dependence among Hecke eigenvalues (D. Kim).- Congruent number triangles with the same hypotenuse (D. Lowry-Duda).- Visualizing modular forms (D. Lowry-Duda).- A Prym variety with everywhere good reduction over Q(√ 61) ( J. Voight).- The S-integral points on the projective line minus three points via étale covers and Skolem's method (B. Poonen).

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Book SynopsisThe chapters in this volume explore the influence of the Russian school on the development of algebraic geometry and representation theory, particularly the pioneering work of two of its illustrious members, Alexander Beilinson and Victor Ginzburg, in celebration of their 60th birthdays. Based on the work of speakers and invited participants at the conference “Interactions Between Representation Theory and Algebraic Geometry”, held at the University of Chicago, August 21-25, 2017, this volume illustrates the impact of their research and how it has shaped the development of various branches of mathematics through the use of D-modules, the affine Grassmannian, symplectic algebraic geometry, and other topics. All authors have been deeply influenced by their ideas and present here cutting-edge developments on modern topics. Chapters are organized around three distinct themes: Groups, algebras, categories, and representation theory D-modules and perverse sheaves Analogous varieties defined by quivers Representation Theory and Algebraic Geometry will be an ideal resource for researchers who work in the area, particularly those interested in exploring the impact of the Russian school.Table of ContentsPart I: Groups, algebras, categories, and their representation theory.- On semisimplification of tensor categories.- Total aspherical parameters for Cherednik algebras.- Microlocal approach to Lusztig's symmetries.- Part II: D-modules and perverse sheaves, particularly on flag varieties and their generalizations.- Fourier-Sato Transform on hyperplane arrangements.- A quasi-coherent description of the category D-mod(Gr GL(n)).- The semi-infinite intersection cohomology sheaf--II: the Ran space version.- A topological approach to Soergel theory.- Part III: Varieties associated to quivers and relations to representation theory and symplectic geometry.- Loop Grassmannians of quivers and affine quantum groups.- Symplectic resolutions for multiplicative quiver varieties and character varieties for punctured surfaces.

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Book SynopsisThis book studies a class of monopoles defined by certain mild conditions, called periodic monopoles of generalized Cherkis–Kapustin (GCK) type. It presents a classification of the latter in terms of difference modules with parabolic structure, revealing a kind of Kobayashi–Hitchin correspondence between differential geometric objects and algebraic objects. It also clarifies the asymptotic behaviour of these monopoles around infinity.The theory of periodic monopoles of GCK type has applications to Yang–Mills theory in differential geometry and to the study of difference modules in dynamical algebraic geometry. A complete account of the theory is given, including major generalizations of results due to Charbonneau, Cherkis, Hurtubise, Kapustin, and others, and a new and original generalization of the nonabelian Hodge correspondence first studied by Corlette, Donaldson, Hitchin and Simpson.This work will be of interest to graduate students and researchers in differential and algebraic geometry, as well as in mathematical physics.Table of Contents. - Introduction. - Preliminaries. - Formal Difference Modules and Good Parabolic Structure. - Filtered Bundles. - Basic Examples of Monopoles Around Infinity. - Asymptotic Behaviour of Periodic Monopoles Around Infinity. - The Filtered Bundles Associated with Periodic Monopoles. - Global Periodic Monopoles of Rank One. - Global Periodic Monopoles and Filtered Difference Modules. - Asymptotic Harmonic Bundles and Asymptotic Doubly Periodic Instantons (Appendix).

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Book SynopsisThis volume is dedicated to Ciro Ciliberto on the occasion of his 70th birthday and contains refereed papers, offering an overview of important parts of current research in algebraic geometry and related research in the history of mathematics. It presents original research as well as surveys, both providing a valuable overview of the current state of the art of the covered topics and reflecting the versatility of the scientific interests of Ciro Ciliberto.Table of ContentsM. C. Brambilla, O. Dumitrescu, E. Postinghel, “Weyl cycles on the blow-up of $P^4$ at eight points".- A. Brigaglia, “Simson’s reconstruction of Apollonius’ Loci Plani. Modern ideas in classical language”.- F. Catanese, “Kummer quartic surfaces, strict self-duality, and more”.- L. Chiantini e Giorgio Ottaviani, “A footnote to a footnote to a paper of B. Segre”.- T. Dedieu and E. Sernesi, “Deformations and extensions of Gorenstein weighted projective spaces”.- V. Di Gennaro and Davide Franco, “Intersection cohomology and Severi Varieties”.- O. Dumitrescu and R. Miranda, “Cremona Orbits in $\mathbb P^4$ and Applications”.- F. Flamini and P. Supino, “On some components of Hilbert schemes of curves”.- Gerard van der Geer, “Siegel modular forms of degree two and three and invariant theory”.- A. Laface and L. Ugaglia, “On intrinsic negative curves”.- Angelo F. Lopez, with an appendix by Thomas Dedieu, “On the extendibility of projective varieties: a survey”.- M. Mella, “The minimal Cremona degree of quartic surfaces”.- M. Mendes Lopes and R. Pardini, “On the degree of the canonical map of a surface of general type”.- C. Pedrini, “Hyperkæhler varieties with a motive of abelian type”.- F. Polizzi and P. Sabatino, “Finite quotients of surface braid groups and double Kodaira fibrations”.- Y. Prokhorov and M. Zaidenberg, “Affine cones over Fano-Mukai fourfolds of genus 10 are flexible”.- J. Roé, “Enriques diagrams under pullback by a double cover”.- E. Rogora, “The “projective spirit” in Segre’s lectures on differential equations”.

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Book SynopsisThis volume celebrates the 100th birthday of Professor Chen-Ning Frank Yang (Nobel 1957), one of the giants of modern science and a living legend. Starting with reminiscences of Yang's time at the research centre for theoretical physics at Stonybrook (now named C. N. Yang Institute) by his successor Peter van Nieuwenhuizen, the book is a collection of articles by world-renowned mathematicians and theoretical physicists. This emphasizes the Dialogue Between Physics and Mathematics that has been a central theme of Professor Yang’s contributions to contemporary science. Fittingly, the contributions to this volume range from experimental physics to pure mathematics, via mathematical physics. On the physics side, the contributions are from Sir Anthony Leggett (Nobel 2003), Jian-Wei Pan (Willis E. Lamb Award 2018), Alexander Polyakov (Breakthrough Prize 2013), Gerard 't Hooft (Nobel 1999), Frank Wilczek (Nobel 2004), Qikun Xue (Fritz London Prize 2020), and Zhongxian Zhao (Bernd T. Matthias Prize 2015), covering an array of topics from superconductivity to the foundations of quantum mechanics. In mathematical physics there are contributions by Sir Roger Penrose (Nobel 2022) and Edward Witten (Fields Medal 1990) on quantum twistors and quantum field theory, respectively. On the mathematics side, the contributions by Vladimir Drinfeld (Fields Medal 1990), Louis Kauffman (Wiener Gold Medal 2014), and Yuri Manin (Cantor Medal 2002) offer novel ideas from knot theory to arithmetic geometry.Inspired by the original ideas of C. N. Yang, this unique collection of papers b masters of physics and mathematics provides, at the highest level, contemporary research directions for graduate students and experts alike.Table of Contents1 Frank Yang at Stony Brook and the Beginning of Supergravity.- 2. A Stacky Approach to Crystals.- 3 The Potts Model, the Jones Polynomial and Link Homology.- 4 The Penrose–Onsager–Yang Approach to Superconductivity and Superfluidity.- 5 Quantum Operads.- 6 Quantum computational complexity withphotons and linear optics.- 7 Quantized Twistors, G2*, and the Split Octonions.- 8 Kronecker Anomalies and Gravitational Striction.- 9 Projecting Local and Global Symmetries to the Planck Scale.- 10 Gauge Symmetry in Shape Dynamics.- 11 Why Does Quantum Field Theory In Curved Spacetime Make Sense? And What Happens To The Algebra of Observables In The Thermodynamic Limit?.- 12 Quantum Anomalous Hall Effect.- 13 Magic Superconducting States in Cuprates.

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Book SynopsisThis book collects the proceedings of a series of conferences dedicated to birational geometry of Fano varieties held in Moscow, Shanghai and PohangThe conferences were focused on the following two related problems:• existence of Kähler–Einstein metrics on Fano varieties• degenerations of Fano varietieson which two famous conjectures were recently proved. The first is the famous Borisov–Alexeev–Borisov Conjecture on the boundedness of Fano varieties, proved by Caucher Birkar (for which he was awarded the Fields medal in 2018), and the second one is the (arguably even more famous) Tian–Yau–Donaldson Conjecture on the existence of Kähler–Einstein metrics on (smooth) Fano varieties and K-stability, which was proved by Xiuxiong Chen, Sir Simon Donaldson and Song Sun. The solutions for these longstanding conjectures have opened new directions in birational and Kähler geometries. These research directions generated new interesting mathematical problems, attracting the attention of mathematicians worldwide.These conferences brought together top researchers in both fields (birational geometry and complex geometry) to solve some of these problems and understand the relations between them. The result of this activity is collected in this book, which contains contributions by sixty nine mathematicians, who contributed forty three research and survey papers to this volume. Many of them were participants of the Moscow–Shanghai–Pohang conferences, while the others helped to expand the research breadth of the volume—the diversity of their contributions reflects the vitality of modern Algebraic Geometry.Table of ContentsT. Abe, Classification of exceptional complements: elliptic curve case.- E. Ballico, E. Gasparim, F. Rubilar, B. Suzuki, LAGRANGIAN SKELETA, COLLARS AND DUALITY.- G. Belousov, CYLINDERS IN DEL PEZZO SURFACES OF DEGREE TWO.- M. Benzerga, FINITENESS OF REAL STRUCTURES ON KLT CALABI-YAU REGULAR SMOOTH PAIRS OF DIMENSION 2.- C. Birkar, ANTICANONICAL VOLUME OF FANO 4-FOLDS.- C. Boyer Christina Tonnesen-Friedman, CONSTANT SCALAR CURVATURE SASAKI METRICS AND PROJECTIVE BUNDLES.- G. Brown, J. Buczynski, A. Kasprzyk, TORIC SARKISOV LINKS.- I. Burban, DU VAL SINGULARITIES.- I. Cheltsov, H. Suess, K-POLYSTABILITY OF TWO SMOOTH FANO THREEFOLDS.- G. Codogni, Z. Patakfalvi, A NOTE ON FAMILIES OF K-SEMISTABLE LOG-FANO PAIRS.- T. Delcroix, THE YAU-TIAN-DONALDSON CONJECTURE FOR COHOMOGENEITY ONE MANIFOLDS.- A. Dubouloz, FIBRATIONS BY AFFINE LINES ON RATIONAL AFFINE SURFACES WITH IRREDUCIBLE BOUNDARIES.- K. Fujita, ON FANO THREEFOLDS OF DEGREE 22 AFTER CHELTSOV AND SHRAMOV.- K. Fujita, Y. Liu, H. Suess, K. Zhang, Z. Zhuang, ON THE CHELTSOV-RUBINSTEIN CONJECTURE.- S. Grishin, Ilya Karzhemanov, Ming-Chang Kang, RATIONALITY OF QUOTIENTS BY FINITE HEISENBERG GROUPS.- Y. Hashimoto.- J. Keller, QUOT-SCHEME LIMIT OF FUBINI–STUDY METRICS AND ITS APPLICATIONS TO BALANCED METRICS.- Z. Hu, EXISTENCE OF CANONICAL MODELS FOR KAWAMATA LOG TERMINAL PAIRS.- Y. Imagi, GENERALIZED THOMAS–YAU UNIQUENESS THEOREMS.- K. Jamieson, BIRATIONALLY RIGID COMPLETE INTERSECTIONS OF CODIMENSION 3.- D. Jeong.- J. Park, SIMPLY CONNECTED SASAKI-EINSTEIN 5-MANIFOLDS: OLD AND NEW.- C. Jiang, CHARACTERIZING Q-FANO THREEFOLDS WITH THE SMALLEST ANTI-CANONICAL VOLUME.- L. Katzarkov, Kyoung-Seog Lee, J. Svoboda, A. Petkov, INTERPRETATIONS OF SPECTRA.- Young-Hoon Kiem, Kyoung-Seog Lee, FANO VISITORS, FANO DIMENSION AND FANO ORBIFOLDS.- In-kyun Kim, N. Viswanathan, J. Won, ON SINGULAR DEL PEZZO HYPERSURFACES OF INDEX 3.- S. Kudryavtsev, Blow-ups of three-dimensional toric singularities.- N. Kurnosov, E. Yasinsky, AUTOMORPHISMS OF HYPERKAHLER MANIFOLDS AND GROUPS ACTING ON CAT(0) SPACES.- A. Laface, R. Quezada, ON GENERALIZED BUCHI SURFACES.- Chi Li, K-STABILITY AND FUJITA APPROXIMATION.- Y. Li, Zhenye Li, ON A CONJECTURE OF FULTON ON ISOTROPIC GRASSMANNIANS.- Y. Maeda, Y. Odaka, FANO SHIMURA VARIETIES WITH MOSTLY BRANCHED CUSP.- L. Makar-Limanov, ON LOCALLY NILPOTENT DERIVATIONS OF DANIELEWSKI DOMAINS.- D. Markouchevitch, A. Moreau, ACTION OF THE AUTOMORPHISM GROUP ON THE JACOBIAN OF KLEIN'S QUARTIC CURVE.- J. Martinez-Garcia, C. Spotti, SOME OBSERVATIONS ON THE DIMENSION OF FANO K-MODULI.- D. Witt Nystrom, OKOUNKOV BODIES AND THE KAHLER GEOMETRY OF PROJECTIVE MANIFOLDS.- J. Park, SINGULARITIES OF PLURI-FUNDAMENTAL DIVISORS ON GORENSTEIN FANO VARIETIES OF COINDEX.- J. Paulhus, A DATABASE OF GROUP ACTIONS ON RIEMANN SURFACES.- A. Petracci, A 1-DIMENSIONAL COMPONENT OF K-MODULI OF DEL PEZZO SURFACES.- T. De Piro, A NON-STANDARD BEZOUT THEOREM FOR CURVES.- Y. Prokhorov, EMBEDDINGS OF THE SYMMETRIC GROUPS TO THE SPACE CREMONA GROUP.- J. Ross, M. Toma, ON HODGE-RIEMANN COHOMOLOGY CLASSES.- Y. Rubinstein, ON LARGE DEVIATION PRINCIPLES AND THE MONGE–AMPERE EQUATION (FOLLOWING BERMAN, HULTGREN).- T. Sano, ON BIRATIONAL BOUNDEDNESS OF SOME CALABI-YAU HYPERSURFACES.- Y. Zarhin, ABELIAN VARIETIES, QUATERNION TRICK AND ENDOMORPHISMS.

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Book SynopsisThis textbook offers an introduction to abelian varieties, a rich topic of central importance to algebraic geometry. The emphasis is on geometric constructions over the complex numbers, notably the construction of important classes of abelian varieties and their algebraic cycles.The book begins with complex tori and their line bundles (theta functions), naturally leading to the definition of abelian varieties. After establishing basic properties, the moduli space of abelian varieties is introduced and studied. The next chapters are devoted to the study of the main examples of abelian varieties: Jacobian varieties, abelian surfaces, Albanese and Picard varieties, Prym varieties, and intermediate Jacobians. Subsequently, the Fourier–Mukai transform is introduced and applied to the study of sheaves, and results on Chow groups and the Hodge conjecture are obtained.This book is suitable for use as the main text for a first course on abelian varieties, for instance as a second graduate course in algebraic geometry. The variety of topics and abundant exercises also make it well suited to reading courses. The book provides an accessible reference, not only for students specializing in algebraic geometry but also in related subjects such as number theory, cryptography, mathematical physics, and integrable systems.Trade Review“The reorganization of the topics is fine surgical work. Several portions of the original monograph are sewn in a natural way in the new book, adding examples or additional text when necessary, and re-arranging the focus to make it a more friendly introduction to the subject. Careful attention to details and the required background makes the book under review accessible to an interested reader and could be a used as textbook for a course on abelian varieties.” (Felipe Zaldivar, MAA Reviews, June 18, 2023)Table of Contents1. Line Bundles on Complex Tori.- 2 Abelian Varieties.- 3 Moduli Spaces.- 4 Jacobian Varieties.- 5 Main Examples of Abelian Varieties.- 6 The Fourier Transform for Sheaves and Cycles.- 7 Introduction to the Hodge Conjecture for Abelian Varieties.

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Book SynopsisThis book provides an elementary introduction, complete with detailed proofs, to the celebrated tilings of the plane discovered by Sir Roger Penrose in the '70s. Quasi-periodic tilings of the plane, of which Penrose tilings are the most famous example, started as recreational mathematics and soon attracted the interest of scientists for their possible application in the description of quasi-crystals. The purpose of this survey, illustrated with more than 200 figures, is to introduce the curious reader to this beautiful topic and be a reference for some proofs that are not easy to find in the literature. The volume covers many aspects of Penrose tilings, including the study, from the point of view of Connes' Noncommutative Geometry, of the space parameterizing these tilings.Table of ContentsIntroduction.- Tilings and puzzles.- Robinson triangles.- Penrose tilings.- De Bruijn’s pentagrids.- The noncommutative space of Penrose tilings.-Some useful formulas.

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Book SynopsisThis book constitutes the proceedings of the Workshop Empowering Novel Geometric Algebra for Graphics and Engineering, ENGAGE 2022, held in conjunction with Computer Graphics International conference, CGI 2022, which took place virtually, in September 2022. The 10 full papers included in this volume were carefully reviewed and selected from 12 submissions. The workshop focused specifically on important aspects of geometric algebra including algebraic foundations, digitized transformations, orientation, conic fitting, protein modelling, digital twinning, and multidimensional signal processing.Table of ContentsFoundations of Geometric Algebra.- Transformations, Orientation and Fitting.- Modelling Proteins and Cities.- Signal Processing with Octonions.

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Book SynopsisSemi-Infinite Geometry is a theory of "doubly infinite-dimensional" geometric or topological objects. In this book the author explains what should be meant by an algebraic variety of semi-infinite nature. Then he applies the framework of semiderived categories, suggested in his previous monograph titled Homological Algebra of Semimodules and Semicontramodules, (Birkhäuser, 2010), to the study of semi-infinite algebraic varieties. Quasi-coherent torsion sheaves and flat pro-quasi-coherent pro-sheaves on ind-schemes are discussed at length in this book, making it suitable for use as an introduction to the theory of quasi-coherent sheaves on ind-schemes. The main output of the homological theory developed in this monograph is the functor of semitensor product on the semiderived category of quasi-coherent torsion sheaves, endowing the semiderived category with the structure of a tensor triangulated category. The author offers two equivalent constructions of the semitensor product, as well as its particular case, the cotensor product, and shows that they enjoy good invariance properties. Several geometric examples are discussed in detail in the book, including the cotangent bundle to an infinite-dimensional projective space, the universal fibration of quadratic cones, and the important popular example of the loop group of an affine algebraic group.Table of Contents- 1. Ind-Schemes and Their Morphisms. - 2. Quasi-Coherent Torsion Sheaves. - 3. Flat Pro-Quasi-Coherent Pro-Sheaves. - 4. Dualizing Complexes on Ind-Noetherian Ind-Schemes. - 5. The Cotensor Product. - 6. Ind-Schemes of Ind-Finite Type and the factorial !-Tensor Product. - 7. X-Flat Pro-Quasi-Coherent Pro-Sheaves on Y. - 8. The Semitensor Product. - 9. Flat Affine Ind-Schemes over Ind-Schemes of Ind-Finite Type. - 10. Invariance Under Postcomposition with a Smooth Morphism. - 11. Some Infinite-Dimensional Geometric Examples.

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Book Synopsis- Introduction.- Koszul duality equivalence.- Categorical DT theory for local surfaces.- D-critical D/K equivalence conjectures.- Categorical wall-crossing via Koszul duality.- Window theorem for DT categories.- Categori ed Hall products on DT categories.- Some auxiliary results.

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Book SynopsisSingularities of bridgeland moduli spaces for k3 categories: an update.- On rigid manifolds of kodaira dimension 1.- On the components of the main stream of the moduli space of surfaces of general type with pg = q = 2.- Degree of irrationality of fano threefold hypersurfaces.- Non effective planar linear systems at the boundary of the mori cone.- Sur l'injectivite de l'application cycle de jannsen.- A prym hypergeometric.- Complete curves in the moduli space of polarized k3 surfaces and hyper-kahler manifolds.- The grothendieck group of algebraic stacks.- Conformal blocks in genus zero and the kz connection.- Second fundamental form and higher gaussian maps.- On infinitesimal invariants of normal functions.- Macaulay duality and its geometry.- On the chow ring of fano fourfolds of k3 type.- Quadratic counts of twisted cubics.

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Book SynopsisOn varieties with ulrich twisted normal bundles.- Rescalability of integrable mixed twistor d-modules.- Cohomology of complete intersections of quadrics.- Generic torelli for coverings of plane quintics ramified in two points.- Theta groups and projective models of hyperkahler varieties.- Footnotes to the birational geometry of primitive symplectic varieties.- Finitude uniforme pour les cycles de codimension 2 sur les corps de nombres.- The hesse pencil and polarizations of type (1,3) on abelian surfaces.- Enriched hodge structures and cycles on complex analytic thickenings.- Notes on the cohomology of local systems of small weight on m_2.- Burnside groups and orbifold invariants of birational maps.- Enumerative geometry of legendrian foliations: a tale of contact.- Geometric representability of 1-cycles on rationally connected threefolds.- Module structure of the k-theory of polynomial-like rings.

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Book Synopsis1 Bill Bruce, Peter Giblin, David Mond, Stephen Pizer and Les Wilson, Jim Damon's Contributions to Singularity Theory and Its Applications.- 2 Viktor A. Vassiliev, Real Function Singularities and Their Bifurcation Sets.- 3 Adam Parusinski and Armin Rainer, Perturbation Theory of Polynomials and Linear Operators.- 4 Goo Ishikawa, Frontal Singularities and Related Problems.- 5 Osamu Saeki, Introduction to Global Singularity Theory of Differentiable Maps.- 6 Claude Sabbah, Singularities of Functions: A Global Point of View.- 7 Mark McLean, Floer Theory, Arc Spaces and Singularities.- 8 Stephen S.-T. Yau and Huaiqing Zuo, Various Derivation Lie Algebras of Isolated Singularities.- 9 Bingyi Chen, Stephen S.-T. Yau and Huaiqing Zuo, Three-Dimensional Rational Isolated Complete Intersection Singularities.- 10 Ziquan Zhuang, Stability of klt Singularities.- 11 Qianyu Chen, Bradley Dirks and Mircea Mustata, An introduction to V-Filtration.- 12 Kiyoshi Takeuchi, Geometric Monodromies, Mixed Hodge Numbers of Motivic Milnor Fibers and Newton Polyhedra.- 13 Willem Veys, Introduction to the Monodromy Conjecture.- 14 Laurentiu G. Maxim, Jose Israel Rodriguez and Botong Wang, Applications of Singularity Theory in Applied Algebraic Geometry and Algebraic Statistics.

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Book SynopsisThis volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009-2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L-functions (and other special functions), investigated in various aspects. Three courses examine some of the most important recent ideas in the positive characteristic theory discovered by Goss (a field in tumultuous development, which is seeing a number of spectacular advances): they cover respectively crystals over function fields (with a number of applications to L-functions of t-motives), gamma and zeta functions in characteristic p, and the binomial theorem. The other two are focused on topics closer to the classical theory of abelian varieties over number fields: they give respectively a thorough introduction to the arithmetic of Jacobians over function fields (including the current status of the BSD conjecture and its geometric analogues, and the construction of Mordell-Weil groups of high rank) and a state of the art survey of Geometric Iwasawa Theory explaining the recent proofs of various versions of the Main Conjecture, in the commutative and non-commutative settings.Table of ContentsCohomological Theory of Crystals over Function Fields and Applications.- On Geometric Iwasawa Theory and Special Values of Zeta Functions.- The Ongoing Binomial Revolution.- Arithmetic of Gamma, Zeta and Multizeta Values for Function Fields.- Curves and Jacobians over Function Fields.

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Book SynopsisThe contributions in this book explore various contexts in which the derived category of coherent sheaves on a variety determines some of its arithmetic. This setting provides new geometric tools for interpreting elements of the Brauer group. With a view towards future arithmetic applications, the book extends a number of powerful tools for analyzing rational points on elliptic curves, e.g., isogenies among curves, torsion points, modular curves, and the resulting descent techniques, as well as higher-dimensional varieties like K3 surfaces. Inspired by the rapid recent advances in our understanding of K3 surfaces, the book is intended to foster cross-pollination between the fields of complex algebraic geometry and number theory.Contributors:· Nicolas Addington · Benjamin Antieau · Kenneth Ascher · Asher Auel · Fedor Bogomolov · Jean-Louis Colliot-Thélène · Krishna Dasaratha · Brendan Hassett · Colin Ingalls · Martí Lahoz · Emanuele Macrì · Kelly McKinnie · Andrew Obus · Ekin Ozman · Raman Parimala · Alexander Perry · Alena Pirutka · Justin Sawon · Alexei N. Skorobogatov · Paolo Stellari · Sho Tanimoto · Hugh Thomas · Yuri Tschinkel · Anthony Várilly-Alvarado · Bianca Viray · Rong ZhouTable of ContentsThe Brauer group is not a derived invariant.- Twisted derived equivalences for affine schemes.- Rational points on twisted K3 surfaces and derived equivalences.- Universal unramified cohomology of cubic fourfolds containing a plane.- Universal spaces for unramified Galois cohomology.- Rational points on K3 surfaces and derived equivalence.- Unramified Brauer classes on cyclic covers of the projective plane.- Arithmetically Cohen-Macaulay bundles on cubic fourfolds containing a plane.- Brauer groups on K3 surfaces and arithmetic applications.- On a local-global principle for H3 of function fields of surfaces over a finite field.- Cohomology and the Brauer group of double covers.

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