“…The main topics discussed are equisingularity of sets and mappings, geometry of singular complex analytic sets, singularities of mappings, characteristic classes, classification of singularities, interaction of singularity theory with some of the new ideas in algebraic geometry imported from theoretical physics, and applications of singularity theory to geometry of surfaces in low dimensional euclidean spaces, to differential equations and to bifurcation theory.…”
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“…It has proved as a means to illustrate the geometric ideas behind the abstract methods of formal algebraic geometry as used by Mumford and Faltings. This book should be of great use to students wishing to enter this field, as well as those already working in it.…”
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“…This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. …”
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“…This work presents applications of numerical semigroups in Algebraic Geometry, Number Theory, and Coding Theory. Background on numerical semigroups is presented in the first two chapters, which introduce basic notation and fundamental concepts and irreducible numerical semigroups. …”
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“…In the area of algebraic geometry, the book gives a detailed account of the Grassmannian varieties, flag varieties, and their Schubert subvarieties. …”
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“…They lie at the crossroads of many areas, including complex analysis, hyperbolic geometry, algebraic geometry, algebra, and arithmetic. The text provides an introduction to the subject from a theoretic and algorithmic perspective. …”
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“…Moduli problems in algebraic geometry date back to Riemann's famous count of the 3g-3 parameters needed to determine a curve of genus g. …”
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“…With its extensive discussion of preliminaries and applications, this book is an ideal resource for graduate students of algebraic geometry and researchers of motivic integration. …”
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“…This book is a scientific record of the eight programs held at MATRIX in 2018: - Non-Equilibrium Systems and Special Functions - Algebraic Geometry, Approximation and Optimisation - On the Frontiers of High Dimensional Computation - Month of Mathematical Biology - Dynamics, Foliations, and Geometry In Dimension 3 - Recent Trends on Nonlinear PDEs of Elliptic and Parabolic Type - Functional Data Analysis and Beyond - Geometric and Categorical Representation Theory The articles are grouped into peer-reviewed contributions and other contributions. …”
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“…Like the first edition, it presents applications of numerical semigroups in Algebraic Geometry, Number Theory and Coding Theory. It starts by discussing the basic notions related to numerical semigroups and those needed to understand semigroups associated with irreducible meromorphic series. …”
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“…This second edition of the book contains two additional more advanced geometric techniques: (1) The modern language and modern view of Algebraic Geometry and (2) Mirror Symmetry. The book grew out of lecture courses. …”
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“…Standard knowledge of algebraic geometry at the level of graduate students is expected. …”
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“…The book offers complete proofs of both Chern’s bound and Trépreau’s algebraization theorem, including all the necessary prerequisites that go beyond elementary complex analysis or basic algebraic geometry. Most of the examples known up to date of non-algebraizable planar webs of maximal rank are discussed in detail. …”
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“…The event brought together emerging and leading researchers at the crossroads of Combinatorics, Topology and Algebra, with a particular focus on new trends in subjects such as: hyperplane arrangements; discrete geometry and combinatorial topology; polytope theory and triangulations of manifolds; combinatorial algebraic geometry and commutative algebra; algebraic combinatorics; and combinatorial representation theory. …”
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“…Moreover, it is extremely important in symplectic geometry and Hamiltonian dynamics, and has strong correlations with mathematical physics, Lie theory and algebraic geometry (including mirror symmetry). As such, the book will appeal to experts with a wide range of backgrounds.…”
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“…Written by leading mathematicians, the papers in this volume cover various topics from algebraic geometry, topology, analysis, operator theory, and representation theory and display the breadth and depth of pure mathematics that has always been characteristic of the Arbeitstagung.…”
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“…The workshop was hosted by the university's Laboratory of Algebra, Cryptology, Algebraic Geometry and Applications, in cooperation with the University of Almería and the University of Málaga. …”
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“…Hyperplane Arrangements will be particularly useful to graduate students and researchers who are interested in algebraic geometry or algebraic topology. The book contains numerous exercises at the end of each chapter, making it suitable for courses as well as self-study.…”
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“…The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, approximation of fractional differential equations, numerical integration formulas, and trigonometric polynomial approximation.…”
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“…The latter include singular integral equations, ordinary and partial differential equations, complex analysis, numerical linear algebra, and real algebraic geometry – all of which were among the topics presented at the 26th International Workshop in Operator Theory and its Applications, held in Tbilisi, Georgia, in the summer of 2015. …”
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