Softcover ISBN: 978-1-4704-7871-1
Product Code: CONM/845
Expected availability date: August 23, 2026
Contemporary Mathematics, Volume: 845;
2026; 308 pp
MSC: Primary 13; 16; 17; 20; 55
This volume contains the proceedings of the AMS Spring Central Sectional Meeting Special Session on Cluster Algebras, Hall Algebras, and Representation Theory, held at the University of Wisconsin-Milwaukee, WI, from April 20–21, 2024.
This volume contains original research articles and survey papers in algebra and representation theory. The contributions address topics including canonical bases and their duals in both cluster algebra and representation-theoretic contexts, representation theory related to the queer Lie superalgebra
, radical Weyl algebras, and finite-dimensional algebras. The volume also
includes a study of Hall algebras under edge contractions allowing edge
loops, as well as a survey on applications of representation theory to
topological data analysis
Graduate students and research mathematicians interested in representation theory.
Jiepeng Fang, Yixin Lan, and Jie Xiao — The correspondence between the canonical and semicanonical bases
Ruoyu Guo — Homological invariants of left and right serial quiver algebras
Fang Li, Jiongkai Pan, and Shijie Zhu — Continuous representations and applications
František Marko and Alexandr N. Zubkov — Representations of queer supergroup
Fan Qin — An introduction to representation-theoretic canonical bases of cluster algebras
Adhish Rele — Hall algebras and edge contractions with loops
Supriya Sharma, R. S. Raja Durai, and Ki-Bong Nam — Generalized Weyl-type algebras and Witt-type
Softcover ISBN: 978-1-4704-8542-9
Product Code: STML/110
Expected availability date: September 06, 2026
Student Mathematical Library Volume: 110;
2026; Estimated: 370 pp
MSC: Primary 65; 14
This book provides an accessible introduction to numerical methods for solving systems of polynomial equations. Similar to how numerical linear algebra turns theorems from linear algebra into floating-point algorithms, numerical algebraic geometry turns theorems from algebraic geometry into numerical algorithms for representing, locating, and manipulating nonlinear algebraic sets.
Numerical Algebraic Geometry begins with an introduction to polynomials and numerics, then carefully builds from a single polynomial in a single variable to isolated solutions of multivariate polynomial systems and ultimately to the computation of positive-dimensional irreducible components. Chapters on applications and advanced topics round out the picture. Exercises are provided throughout both for instructors to assign as homework problems and for readers to deepen their understanding.
Assuming only a background in multivariate calculus and linear algebra, this book would be suitable for an upper-level undergraduate course, motivated undergraduate math majors seeking an independent project, and everyone interested in learning more about numerical algebraic geometry.
Undergraduate students interested in teaching and learning applied algebraic geometry.
Requests
Polynomials and geometry
Numerics and numerical methods
One polynomial in one variable
Isolated solutions of multivariate systems
Irreducible decomposition
Applications
Advanced topics
Bibliography
Index
A co-publication of the AMS and CBMS
Softcover ISBN: 978-1-4704-8535-1
Expected availability date: September 24, 2026
CBMS Regional Conference Series in Mathematics, Volume: 136;
2026; Estimated: 314 pp
MSC: Primary 35; 74
This book develops a rigorous mathematical theory of subwavelength physics derived from first principles, providing a unified framework for the analysis of phenomena arising in metamaterials. It demonstrates the challenges, excitement, and opportunities for research at the interface of mathematics and wave physics.
Based on the 2024 NSF–CBMS conference Mathematical Methods for Novel Metamaterials, held at Auburn University, the volume expands on the first author's CBMS lecture series on the mathematical foundations of subwavelength physics. It is written for graduate students and researchers in mathematics interested in condensed matter theory, wave physics, metamaterials, topological materials, and scattering resonances. The exposition is self-contained and assumes only a standard background in partial differential equations.
Graduate students and researchers interested in the mathematical foundations of condensed matter theory, wave physics, metamaterials, topological materials, and scattering resonances.
Table of Contents
Part 1. Finite systems of subwavelength resonators
Subwavelength resonances
Exceptional points in non-Hermitian systems of subwavelength resonators
Effective medium theory for finite systems of weakly interacting subwavelength resonators
Part 2. Periodic systems of subwavelength resonators
Hermitian systems of subwavelength resonators
Non-Hermitian systems of subwavelength resonators
Part 3. Convergence results for large finite systems of subwavelength resonators
Spectral convergence of defect modes
Convergence to the essential spectrum and band structure
Concluding remarks and open problems
Appendix A. Some basic results
Appendix B. Layer potential techniques
Appendix C. Some technical results and proofs
Bibliography
Index
Hardcover ISBN: 978-1-4704-8580-1
Product Code: GSM/255
Expected availability date: November 07, 2026
Graduate Studies in Mathematics, Volume: 255;
2026; Estimated: 320 pp
MSC: Primary 70; 83
The aim of this book is to give a comprehensive treatment of the majority of important classical field theory from the mathematics perspective. The opening Part 1 gives the exposition of classical mechanics and special relativity that are based on the Hamiltonian approach and emphasizes the Hamiltonian action of the relevant Lie groups.
Part 2 bridges classical mechanics and classical field theory. The authors develop all necessary tools: Lagrangian formulation of classical field theory, conservation laws, the Noether theorem, and Hamiltonian formulation. They present all necessary facts about jet bundles, multivariable calculus of variations, etc.
Part 3 discusses gauge field theory: Maxwell's theory with the abelian structure group
, and Yang–Mills theory with the structure group being semisimple compact Lie groups. For the convenience of the reader, the authors collect all necessary facts about connections and curvature in vector and principal bundles.
In Part 4 the authors briefly discuss the theory of gravity, i.e., Einstein's general relativity. The goal here is to give a coherent mathematical exposition of the basic notions. After careful discussion of properties of the spacetime in general relativity and a standard derivation of Einstein's field equations with matter, the authors discuss the so-called Palatini formalism, an approach to Hilbert–Einstein action when 10 matrix elements of the metric tensor and 40 components of the symmetric Christoffel symbols are independent variables. They also briefly discuss Hamiltonian formalism for Einstein equations and their special solutions, with and without the cosmological constant.
Each chapter in the book concludes with exercises aimed at developing deeper insights into topics discussed in the chapter. Also, each part concludes with a “Notes and References” chapter, which provides references to necessary mathematics background and physics sources.
Undergraduate and graduate students interested in learning and teaching classical field theory.
Foundations of classical mechanics and special relativity
Lagrangian mechanics
Integrals of motion and Noether’s threorem
Integrations of equations of motion
Hamiltonian formalism
Hamiltonian action and moment map
Hamiltonian systems with constraints
Special relativity
Relativistic particle
Spinors and Dirac operator
Notes and references
Basics of classical field theory
Lagrangian formulation of field theory
Conservation laws
Hamiltonian formualtion of classical field theory
Notes and references
Classical gauge theories
Maxwell’s equations
Gauge fixing and Hamiltonian formlaism in electromagnetism
Connections and curvature
Yang-Mills theory
Chern-Simons theory
Notes and references
Theory of gravity
General relativity
Einstein equations
Hamiltonian formulation and exact solutions
Notes and references
Bibliography
Index
Series: Elements in Applied Category Theory
Published: August 2026
Format: Paperback
ISBN: 9781009719995
Format: Hardback
ISBN: 9781009719971
Length: 75 pages
Dimensions: 229 × 152 mm
Availability: Not yet published - available from August 2026
This Element gives an advanced introduction to string diagrams and graph languages for higher-order computation. The subject matter develops in a principled way, starting from the two dimensional syntax of key categorical concepts such as functors, adjunctions, and stricti cation, and leading up to Cartesian Closed Categories, the core mathematical model of the lambda calculus and of functional programming languages. This methodology inverts the usual approach of proceeding from syntax to a categorical interpretation, by rationally reconstructing a syntax from the categorical model. The result is a graph syntax-more precisely, a hierarchical hypergraph syntax-which in many ways is shown to be an improvement over the conventional linear term syntax. The rest of the Element focuses on applications of interest to programming languages: operational semantics, general frameworks for type inference, and complex whole-program transformations such as closure conversion and automatic differentiation. This title is also available as open access on Cambridge Core.
1. Introduction
2. String diagrams
3. Hierarchical string diagrams and the lambda calculus
4. String diagram rewriting
5. Operational semantics of lambda calculi
6. Case studies
References.