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An Alpine Expedition through Algebraic Topology

An Alpine Expedition through Algebraic Topology
Author: Christian Ausoni
Publisher: American Mathematical Soc.
Total Pages: 314
Release: 2014-06-09
Genre: Mathematics
ISBN: 0821891456
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This volume contains the proceedings of the Fourth Arolla Conference on Algebraic Topology, which took place in Arolla, Switzerland, from August 20-25, 2012. The papers in this volume cover topics such as category theory and homological algebra, functor homology, algebraic -theory, cobordism categories, group theory, generalized cohomology theories and multiplicative structures, the theory of iterated loop spaces, Smith-Toda complexes, and topological modular forms.

An Alpine Bouquet of Algebraic Topology

An Alpine Bouquet of Algebraic Topology
Author: Jérôme Scherer
Publisher: American Mathematical Soc.
Total Pages: 308
Release: 2018-05-30
Genre: Algebraic topology
ISBN: 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.

Geometric and Topological Aspects of the Representation Theory of Finite Groups

Geometric and Topological Aspects of the Representation Theory of Finite Groups
Author: Jon F. Carlson
Publisher: Springer
Total Pages: 493
Release: 2018-10-04
Genre: Mathematics
ISBN: 3319940333
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These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled "Groups, Representations, and Cohomology" and held from June 22 to June 27, 2015 at Sabhal Mòr Ostaig on the Isle of Skye, Scotland. The second was a combination of a summer school and workshop on the subject of "Geometric Methods in the Representation Theory of Finite Groups" and took place at the Pacific Institute for the Mathematical Sciences at the University of British Columbia in Vancouver from July 27 to August 5, 2016. The contents of the volume include a composite of both summer school material and workshop-derived survey articles on geometric and topological aspects of the representation theory of finite groups. The mission of the annually sponsored Summer Schools is to train and draw new students, and help Ph.D students transition to independent research.

Lectures on Field Theory and Topology

Lectures on Field Theory and Topology
Author: Daniel S. Freed
Publisher: American Mathematical Soc.
Total Pages: 186
Release: 2019-08-23
Genre: Algebraic topology
ISBN: 1470452065
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These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.

A Handbook of Model Categories

A Handbook of Model Categories
Author: Scott Balchin
Publisher: Springer Nature
Total Pages: 326
Release: 2021-10-29
Genre: Mathematics
ISBN: 3030750353
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This book outlines a vast array of techniques and methods regarding model categories, without focussing on the intricacies of the proofs. Quillen model categories are a fundamental tool for the understanding of homotopy theory. While many introductions to model categories fall back on the same handful of canonical examples, the present book highlights a large, self-contained collection of other examples which appear throughout the literature. In particular, it collects a highly scattered literature into a single volume. The book is aimed at anyone who uses, or is interested in using, model categories to study homotopy theory. It is written in such a way that it can be used as a reference guide for those who are already experts in the field. However, it can also be used as an introduction to the theory for novices.

Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography

Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography
Author: Delaram Kahrobaei
Publisher: American Mathematical Soc.
Total Pages: 136
Release: 2015-02-25
Genre: Business & Economics
ISBN: 0821898590
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This volume contains the proceedings of the AMS Special Session on Algorithmic Problems of Group Theory and Their Complexity, held January 9-10, 2013 in San Diego, CA and the AMS Special Session on Algorithmic Problems of Group Theory and Applications to Information Security, held April 6-7, 2013 at Boston College, Chestnut Hill, MA. Over the past few years the field of group-based cryptography has attracted attention from both group theorists and cryptographers. The new techniques inspired by algorithmic problems in non-commutative group theory and their complexity have offered promising ideas for developing new cryptographic protocols. The papers in this volume cover algorithmic group theory and applications to cryptography.

Geometry, Groups and Dynamics

Geometry, Groups and Dynamics
Author: C. S. Aravinda
Publisher: American Mathematical Soc.
Total Pages: 386
Release: 2015-05-01
Genre: Mathematics
ISBN: 0821898825
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This volume contains the proceedings of the ICTS Program: Groups, Geometry and Dynamics, held December 3-16, 2012, at CEMS, Almora, India. The activity was an academic tribute to Ravi S. Kulkarni on his turning seventy. Articles included in this volume, both introductory and advanced surveys, represent the broad area of geometry that encompasses a large portion of group theory (finite or otherwise) and dynamics in its proximity. These areas have been influenced by Kulkarni's ideas and are closely related to his work and contribution.

Biological Fluid Dynamics: Modeling, Computations, and Applications

Biological Fluid Dynamics: Modeling, Computations, and Applications
Author: Anita T. Layton
Publisher: American Mathematical Soc.
Total Pages: 250
Release: 2014-10-14
Genre: Mathematics
ISBN: 0821898507
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This volume contains the Proceedings of the AMS Special Session on Biological Fluid Dynamics: Modeling, Computation, and Applications, held on October 13, 2012, at Tulane University, New Orleans, Louisiana. In recent years, there has been increasing interest in the development and application of advanced computational techniques for simulating fluid motion driven by immersed flexible structures. That interest is motivated, in large part, by the multitude of applications in physiology and biology. In some biological systems, fluid motion is driven by active biological tissues, which are typically constructed of fibers that are surrounded by fluid. Not only do the fibers hold the tissues together, they also transmit forces that ultimately result in fluid motion. In other examples, the fluid may flow through conduits such as blood vessels or airways that are flexible or active. That is, those conduits may react to and affect the fluid dynamics. This volume responds to the widespread interest among mathematicians, biologists, and engineers in fluid-structure interactions problems. Included are expository and review articles in biological fluid dynamics. Applications that are considered include ciliary motion, upside-down jellyfish, biological feedback in the kidney, peristalsis and dynamic suction pumping, and platelet cohesion and adhesion.

Nonlinear Wave Equations

Nonlinear Wave Equations
Author: Christopher W. Curtis
Publisher: American Mathematical Soc.
Total Pages: 226
Release: 2015-03-26
Genre: Nonlinear wave equations
ISBN: 1470410508
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This volume contains the proceedings of the AMS Special Session on Nonlinear Waves and Integrable Systems, held on April 13-14, 2013, at the University of Colorado, Boulder, Colorado. The field of nonlinear waves is an exciting area of modern mathematical research that also plays a major role in many application areas from physics and fluids. The articles in this volume present a diverse cross section of topics from this field including work on the Inverse Scattering Transform, scattering theory, inverse problems, numerical methods for dispersive wave equations, and analytic and computational methods for free boundary problems. Significant attention to applications is also given throughout the articles with an extensive presentation on new results in the free surface problem in fluids. This volume will be useful to students and researchers interested in learning current techniques in studying nonlinear dispersive systems from both the integrable systems and computational points of view.

Mathematics Going Forward

Mathematics Going Forward
Author: Jean-Michel Morel
Publisher: Springer Nature
Total Pages: 629
Release: 2023-06-14
Genre: Mathematics
ISBN: 3031122445
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This volume is an original collection of articles by 44 leading mathematicians on the theme of the future of the discipline. The contributions range from musings on the future of specific fields, to analyses of the history of the discipline, to discussions of open problems and conjectures, including first solutions of unresolved problems. Interestingly, the topics do not cover all of mathematics, but only those deemed most worthy to reflect on for future generations. These topics encompass the most active parts of pure and applied mathematics, including algebraic geometry, probability, logic, optimization, finance, topology, partial differential equations, category theory, number theory, differential geometry, dynamical systems, artificial intelligence, theory of groups, mathematical physics and statistics.