An Alpine Bouquet of Algebraic Topology
An Alpine Bouquet of Algebraic Topology

Author: Jérôme Scherer

Publisher: American Mathematical Soc.

Published: 2018-05-30

Total Pages: 322

ISBN-13: 147042911X

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This volume contains the proceedings of the Alpine Algebraic and Applied Topology Conference, held from August 15–21, 2016, in Saas-Almagell, Switzerland. The papers cover a broad range of topics in modern algebraic topology, including the theory of highly structured ring spectra, infinity-categories and Segal spaces, equivariant homotopy theory, algebraic -theory and topological cyclic, periodic, or Hochschild homology, intersection cohomology, and symplectic topology.

An Alpine Bouquet of Algebraic Topology
An Alpine Bouquet of Algebraic Topology

Author: Christian Ausoni

Publisher:

Published: 2018

Total Pages: 322

ISBN-13: 9781470447748

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This volume contains the proceedings of the Second Mid-Atlantic Topology Conference, held from March 12–13, 2016, at Johns Hopkins University in Baltimore, Maryland. The focus of the conference, and subsequent papers, was on applications of innovative methods from homotopy theory in category theory, algebraic geometry, and related areas, emphasizing the work of younger researchers in these fields.

New Spaces in Physics: Volume 2
New Spaces in Physics: Volume 2

Author: Mathieu Anel

Publisher: Cambridge University Press

Published: 2021-04-01

Total Pages: 438

ISBN-13: 1108848206

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After the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. This book and its companion explore various new notions of space, including both formal and conceptual points of view, as presented by leading experts at the New Spaces in Mathematics and Physics workshop held at the Institut Henri Poincaré in 2015. This volume covers a broad range of topics in mathematical physics, including noncommutative geometry, supergeometry, derived symplectic geometry, higher geometric quantization, intuitionistic quantum logic, problems with the continuum description of spacetime, twistor theory, loop quantum gravity, and geometry in string theory. It is addressed primarily to mathematical physicists and mathematicians, but also to historians and philosophers of these disciplines.

Algebraic Curves and Their Applications
Algebraic Curves and Their Applications

Author: Lubjana Beshaj

Publisher: American Mathematical Soc.

Published: 2019-02-26

Total Pages: 358

ISBN-13: 1470442477

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This volume contains a collection of papers on algebraic curves and their applications. While algebraic curves traditionally have provided a path toward modern algebraic geometry, they also provide many applications in number theory, computer security and cryptography, coding theory, differential equations, and more. Papers cover topics such as the rational torsion points of elliptic curves, arithmetic statistics in the moduli space of curves, combinatorial descriptions of semistable hyperelliptic curves over local fields, heights on weighted projective spaces, automorphism groups of curves, hyperelliptic curves, dessins d'enfants, applications to Painlevé equations, descent on real algebraic varieties, quadratic residue codes based on hyperelliptic curves, and Abelian varieties and cryptography. This book will be a valuable resource for people interested in algebraic curves and their connections to other branches of mathematics.

Nonassociative Mathematics and its Applications
Nonassociative Mathematics and its Applications

Author: Petr Vojtěchovský

Publisher: American Mathematical Soc.

Published: 2019-01-14

Total Pages: 310

ISBN-13: 1470442450

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Nonassociative mathematics is a broad research area that studies mathematical structures violating the associative law x(yz)=(xy)z. The topics covered by nonassociative mathematics include quasigroups, loops, Latin squares, Lie algebras, Jordan algebras, octonions, racks, quandles, and their applications. This volume contains the proceedings of the Fourth Mile High Conference on Nonassociative Mathematics, held from July 29–August 5, 2017, at the University of Denver, Denver, Colorado. Included are research papers covering active areas of investigation, survey papers covering Leibniz algebras, self-distributive structures, and rack homology, and a sampling of applications ranging from Yang-Mills theory to the Yang-Baxter equation and Laver tables. An important aspect of nonassociative mathematics is the wide range of methods employed, from purely algebraic to geometric, topological, and computational, including automated deduction, all of which play an important role in this book.

Elements of ∞-Category Theory
Elements of ∞-Category Theory

Author: Emily Riehl

Publisher: Cambridge University Press

Published: 2022-02-10

Total Pages: 782

ISBN-13: 1108952194

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The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what exactly an ∞-category is requires various technical models, raising the question of how they might be compared. To overcome this, a model-independent approach is desired, so that theorems proven with any model would apply to them all. This text develops the theory of ∞-categories from first principles in a model-independent fashion using the axiomatic framework of an ∞-cosmos, the universe in which ∞-categories live as objects. An ∞-cosmos is a fertile setting for the formal category theory of ∞-categories, and in this way the foundational proofs in ∞-category theory closely resemble the classical foundations of ordinary category theory. Equipped with exercises and appendices with background material, this first introduction is meant for students and researchers who have a strong foundation in classical 1-category theory.

Handbook of Homotopy Theory
Handbook of Homotopy Theory

Author: Haynes Miller

Publisher: CRC Press

Published: 2020-01-23

Total Pages: 1142

ISBN-13: 1351251600

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The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.

Singular Intersection Homology
Singular Intersection Homology

Author: Greg Friedman

Publisher: Cambridge University Press

Published: 2020-09-24

Total Pages: 823

ISBN-13: 1107150744

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The first expository book-length introduction to intersection homology from the viewpoint of singular and piecewise linear chains.