Softcover ISBN: 978-1-4704-7189-7
Product Code: CONM/815
Contemporary Mathematics Volume: 815;
2025; 159 pp
MSC: Primary 05; 33
This volume contains the proceedings of the AMS Special Session on Macdonald Theory and Beyond: Combinatorics, Geometry, and Integrable Systems, held virtually on March 19?20, 2022.
The articles in this volume represent a number of recent developments in the theory of Macdonald polynomials while highlighting some of its many connections to other areas of mathematics. An important common thread throughout the volume is the role of combinatorial formulas?for Macdonald polynomials themselves as well as operations on them arising from rich additional structures.
The articles of Haglund, Mandelshtam, and Romero concern the type A Macdonald polynomials, which remain a major focus of the subject due to the depth of their combinatorial theory and the power of their specific applications. For arbitrary type Macdonald polynomials, a new combinatorial formula with pseudo-crystal structure is presented in the article of Lenart, Naito, Nomoto, and Sagaki. Finally, the articles of Saied and Wen take up two important new directions in the subject: the SSV polynomials arising from the study of special functions on metaplectic groups, and the wreath Macdonald polynomials associated with certain symplectic resolutions.
Graduate students and research mathematicians interested in Macdonald polynomials, their applications, and generalizations.
J. Haglund ? Combinatorial formulas for (type A) Macdonald polynomials
Cristian Lenart, Satoshi Naito, Fumihiko Nomoto and Daisuke Sagaki ? Symmetric and nonsymmetric Macdonald polynomials via a path model with a pseudo-crystal structure
Joshua Jeishing Wen ? Shuffle approach to wreath Pieri operators
Olya Mandelshtam ? New formulas for Macdonald polynomials via the multispecies exclusion and zero range processes
Marino Romero ? Some combinatorial aspects of Theta and Delta operators
Jason Saied ? A Littlewood-Richardson rule for SSV polynomials
Softcover ISBN: 978-1-4704-7495-9
Contemporary Mathematics Volume: 816;
2025; 170 pp
MSC: Primary 14; 20; 57; 58
This volume contains the proceedings of the AMS Special Session on Singer?Hopf Conjecture in Geometry and Topology, held from March 18?19, 2023, at Georgia Institute of Technology, Atlanta, Georgia. It presents a multidisciplinary point of view on the Singer conjecture, the Hopf conjecture, the study on normalized Betti numbers, and several other intriguing questions on the fundamental group and cohomology of aspherical manifolds.
This volume highlights many interesting research directions in the study of aspherical manifolds and covers a large collection of problems and conjectures about
-invariants of aspherical manifolds. It provides a snapshot of contemporary research in mathematics at the interface of geometry and topology, as well as algebraic geometry. The problems are presented from several distinct points of view, and the articles in this volume suggest possible generalizations and bridge a gap with closely related problems in differential geometry, complex algebraic geometry, and geometric topology.
The volume can play a role in focusing the attention of the mathematical community on these fascinating problems which continue to resist the siege of geometers and topologists.
It is our hope that this volume will become a valuable resource for early career mathematicians interested in these deep and important questions.
Graduate students and research mathematicians interested in geometry and topology of manifolds.
Survey and research articles
Dominik Kirstein, Christian Kremer and Wolfgang Luck ? Some problems and conjectures about
-invariants
Dessislava H. Kochloukova and Stefano Vidussi, with an appendix by Marco Boggi ? Finiteness properties of algebraic fibers of group extensions
Yongqiang Liu ?
-type invariants for complex smooth quasi-projective varieties: A survey
Research articles
Donu Arapura, Lauren?iu G. Maxim and Botong Wang ? Hodge-theoretic variants of the Hopf and Singer conjectures
Alexander Dranishnikov ? On Lipschitz cohomology of aspherical manifolds
Luca F. Di Cerbo and Michael Hull ? Generalized graph manifolds, residual finiteness, and the Singer conjecture
Mark Stern ?
-cohomology and the geometry of
-harmonic forms
Hardcover ISBN: 978-1-4704-7989-3
Colloquium Publications Volume: 68;
2025; 233 pp
MSC: Primary 22; 32; 43
Over the past hundred years, the Heisenberg group has been recognized as an important object in several areas of mathematics, including group representation theory, mathematical physics, complex analysis in several variables, partial differential equations, and differential geometry. This book presents a concise and readable introduction to all these aspects, together with brief descriptions of further research in the area over the past few decades. The author also provides copious references.
Prerequisites for the potential reader are a graduate-level course in modern real analysis, plus the rudiments of functional analysis, Fourier analysis, differential geometry, and Lie groups.
Graduate students and researchers interested in analysis on the Heisenberg group and various applications.
Getting to know the Heisenberg group
Harmonic analysis on the Heisenberg group
Analysis of differential operators
Analysis and geometry of homogeneous spaces
The discrete Heisenberg group: A case study
A glimpse of sub-Riemannian geometry
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN: 978-1-4704-7922-0
Volume: 106; 2025; Estimated: 186 pp
MSC: Primary 00
This book provides an exploration of the mathematics underlying the works of the Catalan architect Antoni Gaudi i Cornet (1852?1926). Illustrated by over 300 graphics and photographs, the text describes the applications of geometry that are found in Gaudi’s buildings. The narrative is further enhanced by numerous “Math Moments,” highlighting the mathematics and mathematicians that come to mind when one observes Gaudi’s creations.
After an opening chapter giving a pictorial overview of Gaudi’s work, the book covers topics from two- and three-dimensional geometry such as plane curves, ruled surfaces, ellipsoids, paraboloids, polygons, and polyhedra. Special attention is given throughout to Gaudi's magnum opus, the Basilica de la Sagrada Familia. The book finishes with detailed appendices, including a brief biography of the architect as well as supplemental proofs and technical notes to develop ideas from the main text.
Suitable for lovers of geometry or architecture, the modest prerequisites mean The Genius of Gaudi can also be used as a supplemental text for a geometry course at the high-school level and above. In addition, it may be enjoyed as a mathematical tour guide for anyone visiting the city of Barcelona.
Underergraduate and graduate students and researchers interested in architecture; connections between mathematics and art/architecture.
Antoni Gaudi the architect
The plane curves
Ruled surfaces
Spheres, ellipsoids, and paraboloids
Polygons
Polyhedra
A Gaudi miscellany
Appendix A. A brief biography of Antoni Gaudi
Appendix B. Chronology
Appendix C. Supplementary proofs
Appendix D. Technical notes
Appendix E. Background for the “Math Moments”
Credits and permissions
Bibliography
Index
Softcover ISBN: 978-1-4704-7552-9
Mathematical Surveys and Monographs Volume: 288;
2025; Estimated: 380 pp
MSC: Primary 37; 35
This monograph offers a comprehensive and accessible treatment of both classical and modern approaches to the stability analysis of nonlinear waves in Hamiltonian systems. Starting with a review of stability of equilibrium points and periodic orbits in finite-dimensional systems, it advances to the infinite-dimensional setting, addressing orbital stability and linearization techniques for spatially decaying and spatially periodic solutions of nonlinear dispersive wave equations, such as the nonlinear Schrodinger, Korteweg?de Vries, and Camassa?Holm equations. The book rigorously develops foundational tools, such as the Vakhitov?Kolokolov slope criterion, the Grillakis?Shatah?Strauss approach, and the integrability methods, but it also introduces innovative adaptations of the stability analysis in problems where conventional methods fall short, including instability of peaked traveling waves and stability of solitary waves over nonzero backgrounds. Aimed at graduate students and researchers, this monograph consolidates decades of research and presents recent advancements in the field, making it an indispensable resource for those studying the stability of nonlinear waves in Hamiltonian systems.
Graduate students and researchers interested in teaching the theory of nonlinear waves, in particular, their stability.
Stability in finite-dimensional systems
Stability of solitary waves
Stability of periodic waves
Orbital stability in integrable Hamiltonian systems
Spectral stability in integrable Hamiltonian systems
Stability of peaked waves
Stability of domain walls and black solitons
Jacobi elliptic functions and integrals
Spectral theory for linear operators
Bibliography
Index
Hardcover ISBN: 978-1-4704-7923-7
Product Code: GSM/251
Graduate Studies in Mathematics Volume: 251;
2025; Estimated: 458 pp
MSC: Primary 47; 46
The theory of positive or completely positive maps from one matrix algebra to another is the mathematical theory underlying the quantum mechanics of finite systems, as well as much of quantum information and computing. Inequalities are fundamental to the subject, and a watershed event in its development was the proof of the strong subadditivity of quantum entropy by Lieb and Ruskai. Over the next 50 years, this result has been extended and refined extensively. The development of the mathematical theory accelerated in the 1990s when researchers began to intensively investigate the quantum mechanical notion of “entanglement” of vectors in tensor products of Hilbert spaces. Entanglement was identified by Schrodinger as a fundamental aspect of quantum mechanics, and in recent decades questions about entanglement have led to much mathematical progress. What has emerged is a beautiful mathematical theory that has very recently arrived at a mature form.
This book is an introduction to that mathematical theory, starting from modest prerequisites. A good knowledge of linear algebra and the basics of analysis and probability are sufficient. In particular, the fundamental aspects of quantum mechanics that are essential for understanding how a number of questions arose are explained from the beginning.
Graduate students and researchers interested in matrix analysis with applications to quantum mechanics, control theory, and quantum computing.
Hilbert space basics
Tensor products of Hilbert spaces
Monotonicity and convexity for operators
von Neumann algebras on finite dimensional Hilbert spaces
Positive linear maps and quantum operators
Some basic trace function inequalities
Fundamental entropy inequalities
Consequences and refinements of SSA
Quantification of entanglement
Convexity, concavity and monotonicity
Majorization methods
Tomita-Takesaki theory and operator inequalities
Convex geometry
Complex interpolation
Bibliography
Index