“…Experienced readers will be interested in the finitary approach to Sturmian words that Christoffel words offer, as well as the novel geometric and algebraic approach chosen for their exposition. They will also appreciate the historical presentation of the Thue-Morse word and its applications, and the novel results on Abelian repetition-free words.…”
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“…This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. …”
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“…This volume thus provides a valuable introduction to multivariate value distribution theory and a survey of some of its results, rich in relations to both algebraic and differential geometry and surely one of the most important branches of the modern geometric theory of functions of a complex variable. …”
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“…It thus provides a general notion of independence (and of rank in the supersimple case) applicable to a wide class of algebraic structures. The basic theory of forking independence is developed, and its properties in a simple structure are analyzed. …”
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“…It begins with an introduction to the geometry of tensors and provides geometric expositions of the basics of quantum information theory, Strassen's laser method for matrix multiplication, and moment maps in algebraic geometry. It also details several exciting recent developments regarding tensors in general. …”
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“…While Tate’s thesis at Princeton in 1950 was finally published in 1967 in the volume Algebraic Number Theory, edited by Cassels and Frohlich, no detailed account of Iwasawa’s work has been published until now, and this volume is intended to fill the gap in the literature of one of the key areas of modern number theory. …”
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“…The relevance of 2-Segal spaces in the study of Hall and Hecke algebras is discussed. Higher Segal Spaces marks the beginning of a program to systematically study d-Segal spaces in all dimensions d. …”
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“…The book is appropriate for a course in discrete Morse theory, a supplemental text to a course in algebraic topology or topological combinatorics, or an independent study.…”
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“…This book studies a large class of topological spaces, many of which play an important role in differential and homotopy topology, algebraic geometry, and catastrophe theory. These include spaces of Morse and generalized Morse functions, iterated loop spaces of spheres, spaces of braid groups, and spaces of knots and links. …”
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“…It focuses on: 1) Feynman integrals and modular functions, 2) hyperbolic and Lorentzian Kac-Moody algebras, related automorphic forms and applications to quantum gravity, 3) superconformal indices and elliptic hypergeometric integrals, related instanton partition functions, 4) moonshine, its arithmetic aspects, Jacobi forms, elliptic genus, and string theory, and 5) theory and applications of the elliptic Painleve equation, and aspects of Painleve equations in quantum field theories. …”
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“…Some pertain primarily to philosophy (as in the works of Plato, Aristotle, Kant, Wittgenstein...), others to general mathematics (Euclid's Elements, Cartesian algebraic geometry, Cantorian infinities, set theory...). …”
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“…The extra geometric richness of the SU(2)-moduli spaces may one day be important for purposes beyond the algebraic invariants that have been studied to date. …”
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“…Thus this construction provides exact solutions of the modified Bianchi identity. By solving algebraically these CFTs we compute the exact tree-level heterotic string spectrum and describe worldsheet non-perturbative effects. …”
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“…In order to elucidate the connections of this formalism to four-dimensional Maxwell-Einstein supergravity theories based on symmetric scalar manifolds (and related to irreducible Euclidean Jordan algebras, the unique exception being the triality-symmetric N = 2 stu model), we then derive a fundamental identity involving the unique rank-4 symmetric invariant tensor of the 0-brane charge symplectic irrepr. of U-duality groups, with potential applications in the quantization of the charge orbits of supergravity theories, as well as in the study of multi-center black hole solutions therein.…”
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“…One of the highlights is the unfolding of modern algebraic and combinatorial structures common to those topics, which give rise to fruitful interactions between theoretical as well as applied and computational perspectives. …”
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“…If all the operators involved are efficient, it suffices to solve an algebraic equation to obtain the final asymmetries. …”
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“…This report describes a possible method to solve this nonlinear, first order differential equation analytically and how to obtain approximate closed algebraic forms, by using the sequence of Gauss integration methods. …”
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“…Our present work proposed a new algorithm for the piecewise-linear approximation of differentiable sensor characteristics with varying algebraic curvature, maintaining the low fixed computational complexity as well as reduced memory requirements, as demonstrated in a test concerning the linearization of the inverse sensor characteristic of type K thermocouple. …”
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“…Our results are graph-theoretic/algebraic in nature. As a first application, we further clarify the binomial structure of (weakly reversible) mass-action systems, arising from chemical reaction networks. …”
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“…Surface modes at the interface between vacuum and the chiral metamaterial exist in their common gap in the wave vector space, which are analytically formulated by algebraic equations. In particular, the surface modes form a pair of spiral surface sheets wrapping around the Weyl cone, resembling the helicoid surface states that occur in topological semimetals. …”
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