*Presents the current state of knowledge in all aspects of two-dimensional homotopy theory. Useful for both students and experts.*

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# Advances in Two Dimensional Homotopy and Combinatorial Group Theory

This volume presents the current state of knowledge in all aspects of two-dimensional homotopy theory. Building on the foundations laid a quarter of a century ago in the volume Two-dimensional Homotopy and Combinatorial Group Theory (LMS 197), the editors here bring together much remarkable progress that has been obtained in the intervening years. And while the fundamental open questions, such as the Andrews-Curtis Conjecture and the Whitehead asphericity problem remain to be (fully) solved, this book will provide both students and experts with an overview of the state of the art and work in progress. Ample references are included to the LMS 197 volume, as well as a comprehensive bibliography bringing matters entirely up to date.
# Two Dimensional Homotopy and Combinatorial Group Theory

This book considers the current state of knowledge in the geometric and algebraic aspects of two-dimensional homotopy theory.
# Surveys in Combinatorics 2021

These nine articles provide up-to-date surveys of topics of contemporary interest in combinatorics.
# Co end Calculus

This easy-to-cite handbook gives the first systematic treatment of the (co)end calculus in category theory and its applications.
# Equivariant Topology and Derived Algebra

A collection of research papers, both new and expository, based on the interests of Professor J. P. C. Greenlees.
# Computational Cryptography

A guide to cryptanalysis and the implementation of cryptosystems, written for students and security engineers by leading experts.
# Topological Methods in Group Theory

Details some of the most recent developments at the interface of topology and geometric group theory. Ideal for graduate students.
# Surveys in Combinatorics 2019

Eight articles provide a valuable survey of the present state of knowledge in combinatorics.
# Integrable Systems and Algebraic Geometry

Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. The articles in this second volume discuss areas related to algebraic geometry, emphasizing the connections of this central subject to integrable systems, arithmetic geometry, Riemann surfaces, coding theory and lattice theory.
# Advances in Elliptic Curve Cryptography

Since the appearance of the authors' first volume on elliptic curve cryptography in 1999 there has been tremendous progress in the field. In some topics, particularly point counting, the progress has been spectacular. Other topics such as the Weil and Tate pairings have been applied in new and important ways to cryptographic protocols that hold great promise. Notions such as provable security, side channel analysis and the Weil descent technique have also grown in importance. This second volume addresses these advances and brings the reader up to date. Prominent contributors to the research literature in these areas have provided articles that reflect the current state of these important topics. They are divided into the areas of protocols, implementation techniques, mathematical foundations and pairing based cryptography. Each of the topics is presented in an accessible, coherent and consistent manner for a wide audience that will include mathematicians, computer scientists and engineers.
# Groups St Andrews 2017 in Birmingham

These proceedings of 'Groups St Andrews 2017' provide a snapshot of the state-of-the-art in contemporary group theory.
# Partial Differential Equations in Fluid Mechanics

The Euler and Navier–Stokes equations are the fundamental mathematical models of fluid mechanics, and their study remains central in the modern theory of partial differential equations. This volume of articles, derived from the workshop 'PDEs in Fluid Mechanics' held at the University of Warwick in 2016, serves to consolidate, survey and further advance research in this area. It contains reviews of recent progress and classical results, as well as cutting-edge research articles. Topics include Onsager's conjecture for energy conservation in the Euler equations, weak-strong uniqueness in fluid models and several chapters address the Navier–Stokes equations directly; in particular, a retelling of Leray's formative 1934 paper in modern mathematical language. The book also covers more general PDE methods with applications in fluid mechanics and beyond. This collection will serve as a helpful overview of current research for graduate students new to the area and for more established researchers.
# Shimura Varieties

A concise and comprehensive introduction to trace formula methods in the study of Shimura varieties and associated Galois representations.
# New Directions in Locally Compact Groups

This collection of expository articles by a range of established experts and newer researchers provides an overview of the recent developments in the theory of locally compact groups. It includes introductory articles on totally disconnected locally compact groups, profinite groups, p-adic Lie groups and the metric geometry of locally compact groups. Concrete examples, including groups acting on trees and Neretin groups, are discussed in detail. An outline of the emerging structure theory of locally compact groups beyond the connected case is presented through three complementary approaches: Willis' theory of the scale function, global decompositions by means of subnormal series, and the local approach relying on the structure lattice. An introduction to lattices, invariant random subgroups and L2-invariants, and a brief account of the Burger–Mozes construction of simple lattices are also included. A final chapter collects various problems suggesting future research directions.
# Permutation Groups and Cartesian Decompositions

Concise introduction to permutation groups, focusing on invariant cartesian decompositions and applications in algebra and combinatorics.
# Wigner Type Theorems for Hilbert Grassmannians

An accessible introduction to the geometric approach to Wigner's theorem and its role in quantum mechanics.
# Integrable Systems and Algebraic Geometry

A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.
# Integrable Systems and Algebraic Geometry

Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. This first volume covers a wide range of areas related to integrable systems, often emphasizing the deep connections with algebraic geometry. Common themes include theta functions and Abelian varieties, Lax equations, integrable hierarchies, Hamiltonian flows and difference operators. These powerful tools are applied to spinning top, Hitchin, Painleve and many other notable special equations.
# Partial Differential Equations arising from Physics and Geometry

Presents the state of the art in PDEs, including the latest research and short courses accessible to graduate students.
# Analysis and Geometry on Graphs and Manifolds

The interplay of geometry, spectral theory and stochastics has a long and fruitful history, and is the driving force behind many developments in modern mathematics. Bringing together contributions from a 2017 conference at the University of Potsdam, this volume focuses on global effects of local properties. Exploring the similarities and differences between the discrete and the continuous settings is of great interest to both researchers and graduate students in geometric analysis. The range of survey articles presented in this volume give an expository overview of various topics, including curvature, the effects of geometry on the spectrum, geometric group theory, and spectral theory of Laplacian and Schrödinger operators. Also included are shorter articles focusing on specific techniques and problems, allowing the reader to get to the heart of several key topics.