Contemporary Mathematics, Volume: 746;
2020; 246 pp; Softcover
MSC: Primary 57; 05; 92; 82; 65;
Print ISBN: 978-1-4704-4840-0
Product Code: CONM/746
This book contains the proceedings of the AMS Special Session on Topology of Biopolymers, held from April 21?22, 2018, at Northeastern University, Boston, MA.
The papers cover recent results on the topology and geometry of DNA and protein knotting using techniques from knot theory, spatial graph theory, differential geometry, molecular simulations, and laboratory experimentation. They include current work on the following topics: the density and supercoiling of DNA minicircles; the dependence of DNA geometry on its amino acid sequence; random models of DNA knotting; topological models of DNA replication and recombination; theories of how and why proteins knot; topological and geometric approaches to identifying entanglements in proteins; and topological and geometric techniques to predict protein folding rates.
All of the articles are written as surveys intended for a broad interdisciplinary audience with a minimum of prerequisites. In addition to being a useful reference for experts, this book also provides an excellent introduction to the fast-moving field of topology and geometry of biopolymers.
Graduate students and research mathematicians interested in applications of topology and DNA proteins.
Graduate Studies in Mathematics, Volume: 206;
2020; 790 pp; Hardcover
MSC: Primary 53; 58; 52; 35;
Print ISBN: 978-1-4704-5596-5
Product Code: GSM/206
Extrinsic geometric flows are characterized by a submanifold evolving in an ambient space with velocity determined by its extrinsic curvature. The goal of this book is to give an extensive introduction to a few of the most prominent extrinsic flows, namely, the curve shortening flow, the mean curvature flow, the Gaus curvature flow, the inverse-mean curvature flow, and fully nonlinear flows of mean curvature and inverse-mean curvature type. The authors highlight techniques and behaviors that frequently arise in the study of these (and other) flows. To illustrate the broad applicability of the techniques developed, they also consider general classes of fully nonlinear curvature flows.
The book is written at the level of a graduate student who has had a basic course in differential geometry and has some familiarity with partial differential equations. It is intended also to be useful as a reference for specialists. In general, the authors provide detailed proofs, although for some more specialized results they may only present the main ideas; in such cases, they provide references for complete proofs. A brief survey of additional topics, with extensive references, can be found in the notes and commentary at the end of each chapter.
Graduate students and researchers interested in mean curvature flow.
Contemporary Mathematics, Volume: 747;
2020; 240 pp; Softcover
MSC: Primary 81; 16; 20; 18; 19;
Print ISBN: 978-1-4704-4074-9
Product Code: CONM/747
This volume contains the proceedings of the AMS Special Session on Topological Phases of Matter and Quantum Computation, held from September 24?25, 2016, at Bowdoin College, Brunswick, Maine.
Topological quantum computing has exploded in popularity in recent years. Sitting at the triple point between mathematics, physics, and computer science, it has the potential to revolutionize sub-disciplines in these fields. The academic importance of this field has been recognized in physics through the 2016 Nobel Prize. In mathematics, some of the 1990 Fields Medals were awarded for developments in topics that nowadays are fundamental tools for the study of topological quantum computation. Moreover, the practical importance of this discipline has been underscored by recent industry investments.
The relative youth of this field combined with a high degree of interest in it makes now an excellent time to get involved. Furthermore, the cross-disciplinary nature of topological quantum computing provides an unprecedented number of opportunities for cross-pollination of mathematics, physics, and computer science. This can be seen in the variety of works contained in this volume. With articles coming from mathematics, physics, and computer science, this volume aims to provide a taste of different sub-disciplines for novices and a wealth of new perspectives for veteran researchers. Regardless of your point of entry into topological quantum computing or your experience level, this volume has something for you.
Graduate students and research mathematicians interested in quantum computation, quantum field theories, and topological quantum computation.
Contemporary Mathematics, Volume: 748;
2020; 200 pp; Softcover
MSC: Primary 31; 33; 35; 39; 42; 46; 76; 78;
Print ISBN: 978-1-4704-4896-7
Product Code: CONM/748
This volume contains the proceedings of the AMS Special Session on Harmonic Analysis and Partial Differential Equations, held from April 21?22, 2018, at Northeastern University, Boston, Massachusetts.
The book features a series of recent developments at the interface between harmonic analysis and partial differential equations and is aimed toward the theoretical and applied communities of researchers working in real, complex, and harmonic analysis, partial differential equations, and their applications.
The topics covered belong to the general areas of the theory of function spaces, partial differential equations of elliptic, parabolic, and dissipative types, geometric optics, free boundary problems, and ergodic theory, and the emphasis is on a host of new concepts, methods, and results.
Graduate students and research mathematicians interested in harmonic analysis and partial differential equations.
University Lecture Series, Volume: 74;
2020; 128 pp; Softcover
MSC: Primary 55; 58; 53;
Print ISBN: 978-1-4704-5495-1
Product Code: ULECT/74
The theory of persistence modules originated in topological data analysis and became an active area of research in algebraic topology. This book provides a concise and self-contained introduction to persistence modules and focuses on their interactions with pure mathematics, bringing the reader to the cutting edge of current research. In particular, the authors present applications of persistence to symplectic topology, including the geometry of symplectomorphism groups and embedding problems. Furthermore, they discuss topological function theory, which provides new insight into oscillation of functions. The book is accessible to readers with a basic background in algebraic and differential topology.
Graduate students and researchers interested in applications of new methods of computational topology to function theory and symplectic geometry.
Mathematical Surveys and Monographs, Volume: 246;
2020; 246 pp; Hardcover
MSC: Primary 34; 35; Secondary 37
Print ISBN: 978-1-4704-5308-4
Product Code: SURV/246
This book provides a comprehensive study of how attractors behave under perturbations for both autonomous and non-autonomous problems. Furthermore, the forward asymptotics of non-autonomous dynamical systems is presented here for the first time in a unified manner.
When modelling real world phenomena imprecisions are unavoidable. On the other hand, it is paramount that mathematical models reflect the modelled phenomenon, in spite of unimportant neglectable influences discounted by simplifications, small errors introduced by empirical laws or measurements, among others.
The authors deal with this issue by investigating the permanence of dynamical structures and continuity properties of the attractor. This is done in both the autonomous (time independent) and non-autonomous (time dependent) framework in four distinct levels of approximation: the upper semicontinuity, lower semicontinuity, topological structural stability and geometrical structural stability.
This book is aimed at graduate students and researchers interested in dissipative dynamical systems and stability theory, and requires only a basic background in metric spaces, functional analysis and, for the applications, techniques of ordinary and partial differential equations.
Graduate students and researchers interested in dynamical systems.