This book provides an introduction to hyperbolic geometry in dimension three, with motivation and applications arising from knot theory. Hyperbolic geometry was first used as a tool to study knots by Riley and then Thurston in the 1970s. By the 1980s, combining work of Mostow and Prasad with Gordon and Luecke, it was known that a hyperbolic ......
This book introduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the concept of curvature via the Jacobi equation which, through discussion of tidal forces, further helps motivate the Einstein field equations. After addressing concepts in geometry such as ......
This book is an introductory text that charts the recent developments in the area of Whitney-type extension problems and the mathematical aspects of interpolation of data. It provides a detailed tour of a new and active area of mathematical research. In each section, the authors focus on a different key insight in the theory. The book motivates ......
This volume contains the proceedings of a conference celebrating the work of Steven Boyer, held from June 2-8, 2018, at Universite du Quebec a Montreal, Montreal, Quebec, Canada. Boyer's contributions to research in low-dimensional geometry and topology, and to the Canadian mathematical community, were recognized during the conference. The ......
Unitary representations of groups play an important role in many subjects, including number theory, geometry, probability theory, partial differential equations, and quantum mechanics. This monograph focuses on dual spaces associated to a group, which are spaces of building blocks of general unitary representations. Special attention is paid to ......
This volume contains the proceedings of the AMS Special Session on Geometry of Submanifolds, in honor or Bang-Yen Chen's 75th birthday, held from October 20-21, 2018, at the University of Michigan, Ann Arbor, Michigan. The development of contemporary geometry of submanifolds benefited greatly from Bang-Yen Chen's contributions, as several ......
It presents several themes of contemporary representation theory together with some new tools, such as stable ?-categories, stable derivators, and contramodules. In the first part, expanded lecture notes of four courses delivered at the workshop are presented, covering the representation theory of finite sets with correspondences, geometric theory ......
The articles cover new developments in control theory and inverse problems. First, the problem of Calderon, which consists of determining a conductivity appearing in an elliptic equation from excitation and measurements on a part of the boundary of the domain, is studied. Second, an introduction to the mathematical analysis of inverse spectral ......
A polynomial identity for an algebra (or a ring) $A$ is a polynomial in noncommutative variables that vanishes under any evaluation in $A$. An algebra satisfying a nontrivial polynomial identity is called a PI algebra, and this is the main object of study in this book, which can be used by graduate students and researchers alike. The book is ......
