“…The important advantage of this approach is that it allows the separation of the role of high differentiability and that of algebraic geometry in a smooth setting: all the geometrically relevant phenomena appear already for polynomial mappings. …”
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“…The results concerning ordinary differential equations are then extended to control problems described by differential-algebraic equations in a comprehensive way for the first time in the literature.…”
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“…On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. …”
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“…Its aim was to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. …”
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“…Applications of Galois theory to solvability of algebraic equations by radicals, basics of Picard–Vessiot theory, and Liouville's results on the class of functions representable by quadratures are also discussed. …”
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“…Though the proof of the Hodge Theorem is omitted, its consequences - topological, geometrical and algebraic - are discussed at some length. The special properties of complex projective manifolds constitute an important body of knowledge and readers are guided through it with the help of selected exercises. …”
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“…This book seeks to bring this information to students and researchers in geometry and analysis on causal symmetric spaces.Includes the newest results in harmonic analysis including Spherical functions on ordered symmetric space and the holmorphic discrete series and Hardy spaces on compactly casual symmetric spacesDeals with the infinitesimal situation, coverings of symmetric spaces, classification of causal symmetric pairs and invariant cone fieldsPresents basic geometric properties of semi-simple symmetric spacesIncludes appendices on Lie algebras and Lie groups, Bounded symmetric domains (Cayley transforms), Antiholomorphic Involutions on Bounded Domains and Para-Hermitian Symmetric Spaces…”
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“…Graduate students (and some undergraduates) with sufficient knowledge of basic general topology, basic topological dynamics, and basic algebraic topology will find little difficulty in reading this book.…”
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“…The paper contains proofs of most important results in transcendence theory and diophantine analysis, notably Siegel’s celebrated theorem on integral points on algebraic curves. Many modern versions of Siegel’s proof have appeared, but none seem to faithfully reproduce all features of the original one. …”
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“…Heath-Brown's lecture notes mainly deal with counting integer solutions to Diophantine equations, using among other tools several results from algebraic geometry and from the geometry of numbers. …”
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“…In later chapters more modern issues on heights of algebraic points are dealt with, and applied to a sharp quantitative treatment of the unit equation. …”
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“…While some familiarity with algebraic topology and sheaf theory is assumed, the notes include a self-contained account of further material on constructibility, derived categories, Verdier duality, biduality, and on stratified spaces, which is used in the second paper but not found in standard texts. …”
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“…The material covered includes the Wedderburn-Artin theory of semisimple rings, Jacobson's theory of the radical, representation theory of groups and algebras, prime and semiprime rings, local and semilocal rings, perfect and semiperfect rings, etc. …”
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“…The text covers useful numerical methods, including interpolation, Simpson’s rule on integration, the Gauss elimination method for solving systems of linear algebraic equations, the Runge-Kutta method for solving ordinary differential equations, and the search method in combination with the bisection method for obtaining the roots of transcendental and polynomial equations. …”
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“…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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“…This book offers an original contribution to the foundations of logic and mathematics, and focuses on the internal logic of mathematical theories, from arithmetic or number theory to algebraic geometry. Arithmetical logic is the term used to refer to the internal logic of classical arithmetic, here called Fermat-Kronecker arithmetic, and combines Fermat’s method of infinite descent with Kronecker’s general arithmetic of homogeneous polynomials. …”
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“…This book provides the first concise and self-contained introduction to the theory on the simplest yet very nontrivial example of the infinite symmetric group, focusing on its deep connections to probability, mathematical physics, and algebraic combinatorics. Following a discussion of the classical Thoma's theorem which describes the characters of the infinite symmetric group, the authors describe explicit constructions of an important class of representations, including both the irreducible and generalized ones. …”
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“…In its first chapter of the book presents an introduction to Synchronization of LSNSs and Algebraic Graph Theory as well as an overview of recent developments of LSNSs with sampled data control or output regulation control. …”
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“…Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems. …”
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“…Furthermore, the techniques used to rigorously establish the expansion property of a graph draw from such diverse areas of mathematics as representation theory, algebraic geometry, and arithmetic combinatorics. This text focuses on the latter topic in the important case of Cayley graphs on finite groups of Lie type, developing tools such as Kazhdan's property (T), quasirandomness, product estimates, escape from subvarieties, and the Balog-Szemerédi-Gowers lemma. …”
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