Softcover ISBN: 978-1-4704-7034-0
Product Code: CONM/791
Expected availability date: March 18, 2024
Contemporary Mathematics Volume: 791
2024; 227 pp
MSC: Primary 14; 16; 17; 35; 18; 57;
This volume contains the proceedings of the virtual AMS Special Session on Geometric and Algebraic Aspects of Quantum Groups and Related Topics, held from November 20?21, 2021.
Noncommutative algebras and noncommutative algebraic geometry have been an active field of research for the past several decades, with many important applications in mathematical physics, representation theory, number theory, combinatorics, geometry, low-dimensional topology, and category theory.
Papers in this volume contain original research, written by speakers and their collaborators. Many papers also discuss new concepts with detailed examples and current trends with novel and important results, all of which are invaluable contributions to the mathematics community.
Graduate students and research mathematicians interested in representation theory of noncommutative algebras and its applications to various areas of mathematical physics, topology, geometry, and number theory.
Jacob Glidewell, William E. Hurst, Kyungyong Lee and Li Li - On the two-dimensional Jacobian conjecture: Magnusf formula revisited, III
Tolulope Oke - Homotopy lifting maps on Hochschild cohomology and connections to deformation of algebras using reduction systems
Jason Gaddis and Thomas Lamkin - Centers and automorphisms of PI quantum matrix algebras
Garrett Johnson and Hayk Melikyan - On automorphisms of quantum Schubert cells
Anton M. Zeitlin - On Wronskians and qq
-systems
Mee Seong Im and Mikhail Khovanov - One-dimensional topological theories with defects: the linear case
Mikhail Khovanov and Nitu Kitchloo - A deformation of Robert-Wagner foam evaluation and link homology
Mikhail Khovanov, Krzysztof Putyra and Pedro Vaz - Odd two-variable Soergel bimodules and Rouquier complexes
Softcover ISBN: 978-1-4704-7140-8
Product Code: CONM/792
Expected availability date: March 18, 2024
Contemporary Mathematics Volume: 792
MSC: Primary 11; 42; 32;
This volume contains the proceedings of the virtual AMS Special Session on Harmonic Analysis, held from March 26?27, 2022.
Harmonic analysis has gone through rapid developments in the past decade. New tools, including multilinear Kakeya inequalities, broad-narrow analysis, polynomial methods, decoupling inequalities, and refined Strichartz inequalities, are playing a crucial role in resolving problems that were previously considered out of reach. A large number of important works in connection with geometric measure theory, analytic number theory, partial differential equations, several complex variables, etc., have appeared in the last few years. This book collects some examples of this work.
Graduate students and research mathematicians interested in harmonic analysis, geometric measure theory, analytic number theory, and several complex variables.
Hardcover ISBN: 978-1-4704-6105-8
Product Code: GSM/239
Expected availability date: April 03, 2024
Graduate Studies in Mathematics Volume: 239
2024; 363 pp
MSC: Primary 58;
In differential geometry and topology one often deals with systems of partial differential equations as well as partial differential inequalities that have infinitely many solutions whatever boundary conditions are imposed. It was discovered in the 1950s that the solvability of differential relations (i.e., equations and inequalities) of this kind can often be reduced to a problem of a purely homotopy-theoretic nature. One says in this case that the corresponding differential relation satisfies the h
-principle. Two famous examples of the h
-principle, the Nash?Kuiper C1
-isometric embedding theory in Riemannian geometry and the Smale?Hirsch immersion theory in differential topology, were later transformed by Gromov into powerful general methods for establishing the h
-principle.
The authors cover two main methods for proving the h
-principle: holonomic approximation and convex integration. The reader will find that, with a few notable exceptions, most instances of the h
-principle can be treated by the methods considered here. A special emphasis is made on applications to symplectic and contact geometry.
The present book is the first broadly accessible exposition of the theory and its applications, making it an excellent text for a graduate course on geometric methods for solving partial differential equations and inequalities. Geometers, topologists, and analysts will also find much value in this very readable exposition of an important and remarkable topic.
This second edition of the book is significantly revised and expanded to almost twice of the original size. The most significant addition to the original book is the new part devoted to the method of wrinkling and its applications. Several other chapters (e.g., on multivalued holonomic approximation and foliations) are either added or completely rewritten.
Graduate students and researchers interested in recent advances in differential topology.
Hardcover ISBN: 978-1-4704-7420-1
Product Code: GSM/240
Expected availability date: April 17, 2024
Graduate Studies in Mathematics Volume: 240
2024
MSC: Primary 35; Secondary 52; 49;
This book presents a systematic analysis of the Monge?Ampere equation, the linearized Monge?Ampere equation, and their applications, with emphasis on both interior and boundary theories. Starting from scratch, it gives an extensive survey of fundamental results, essential techniques, and intriguing phenomena in the solvability, geometry, and regularity of Monge?Ampere equations. It describes in depth diverse applications arising in geometry, fluid mechanics, meteorology, economics, and the calculus of variations.
The modern treatment of boundary behaviors of solutions to Monge?Ampere equations, a very important topic of the theory, is thoroughly discussed. The book synthesizes many important recent advances, including Savin's boundary localization theorem, spectral theory, and interior and boundary regularity in Sobolev and Holder spaces with optimal assumptions. It highlights geometric aspects of the theory and connections with adjacent research areas.
This self-contained book provides the necessary background and techniques in convex geometry, real analysis, and partial differential equations, presents detailed proofs of all theorems, explains subtle constructions, and includes well over a hundred exercises. It can serve as an accessible text for graduate students as well as researchers interested in this subject.
Graduate students and researchers interested in non-linear PDE.
available from March 2024
FORMAT: Paperback ISBN: 9781009436212
This book provides statistics instructors and students with complete classroom material for a one- or two-semester course on applied regression and causal inference. It is built around 52 stories, 52 class-participation activities, 52 hands-on computer demonstrations, and 52 discussion problems that allow instructors and students to explore in a fun way the real-world complexity of the subject. The book fosters an engaging 'flipped classroom' environment with a focus on visualization and understanding. The book provides instructors with frameworks for self-study or for structuring the course, along with tips for maintaining student engagement at all levels, and practice exam questions to help guide learning. Designed to accompany the authors' previous textbook Regression and Other Stories, its modular nature and wealth of material allow this book to be adapted to different courses and texts or be used by learners as a hands-on workbook.
Connects statistical ideas and methods to real-world applications with fifty-two stories
Helps students stay focused with group activities and stopping points for classroom discussion
Provides data and code for hands-on computer demonstrations in R, which can be shown by the instructor or done individually by students
Helps students master basic skills with quick questions and drills
Can be adjusted to statistics courses at different levels and speeds
'This book is an extraordinarily rich and generous resource for teaching statistics. Full of stories about challenging statistical problems, the examples reflect all the messiness of real life, and encourage class discussion of what went wrong and how to do things better. The extensive collection of lesson plans and exercises provides a fine inspiration to adopt a different, more active, style of teaching.' David Spiegelhalter, University of Cambridge
'This is a wonderful read for any statistics teacher. The focus on real-world applications and statistical thinking ensures that everyone will gain new insights and perspectives no matter how long you have been teaching.' Beth Chance, California Polytechnic State University
'I have to say reading this book came as a pleasant surprise for me. I thought I was going to be reviewing another statistics book and instead, it was an insightful read on how to think about teaching statistics. I found it engaging and helpful in rethinking how I approach teaching statistics.' Pamela Davis-Kean, University of Michigan
How to use this book
Part I. Organizing a Plan of Study:
1. Active learning
2. Setting up a course of study
3. In the classroom
Part II. Stories, Activities, Problems, and Demonstrations:
4. Week by week: the first semester
5. Week by week: the second semester
Appendixes: A. Pre-test questions
B. Final exam questions
C. Outlines of classroom activities.
*
Part of Cambridge Studies in Advanced Mathematics
Not yet published - available from February 2024
FORMAT: Hardback ISBN: 9781108836623
Discrete structures model a vast array of objects ranging from DNA sequences to internet networks. The theory of generating functions provides an algebraic framework for discrete structures to be enumerated using mathematical tools. This book is the result of 25 years of work developing analytic machinery to recover asymptotics of multivariate sequences from their generating functions, using multivariate methods that rely on a combination of analytic, algebraic, and topological tools. The resulting theory of analytic combinatorics in several variables is put to use in diverse applications from mathematics, combinatorics, computer science, and the natural sciences. This new edition is even more accessible to graduate students, with many more exercises, computational examples with Sage worksheets to illustrate the main results, updated background material, additional illustrations, and a new chapter providing a conceptual overview.
Develops classical tools in topology and analysis from a computational point of view to motivate the study of abstract mathematical theories, and to show how pure mathematics can be applied to concrete applications in mathematics, computer science, and the natural sciences
Provides an exposition that weaves in the considerable background material in a way that a graduate student can successfully tackle
Allows readers to replicate computations and check their work in Sage worksheets
Comprehensively surveys forty years of development of an emerging field, and shows that combinatorial problems can draw together many fields of mathematics, including algebraic geometry, harmonic analysis, and singularity theory
'A definitive treatment of a challenging but very useful subject. There is a wide variety of situations calling for the estimation of the coefficients of a multivariate generating function. The authors have done a superb job of classifying and elucidating the myriad of available techniques for achieving this aim.' Richard P. Stanley, University of Miami
'This book is an invaluable resource that is certain to have dramatic impact on research and teaching in this rapidly developing area of mathematics. The first edition broke new ground; this edition prepares the field for others to harvest new knowledge with important applications in many scientific disciplines.'
Part I. Combinatorial Enumeration:
1. Introduction
2. Generating functions
3. Univariate asymptotics
Part II. Mathematical Background:
4. Fourier?Laplace integrals in one variable
5. Multivariate Fourier?Laplace integrals
6. Laurent series, amoebas, and convex geometry
Part III. Multivariate Enumeration:
7. Overview of analytic methods for multivariate generating functions
8. Effective computations and ACSV
9. Smooth point asymptotics
10. Multiple point asymptotics
11. Cone point asymptotics
12. Combinatorial applications
13. Challenges and extensions
Appendices: A. Integration on manifolds
B. Algebraic topology
C. Residue forms and classical Morse theory
D. Stratification and stratified Morse theory
References
Author index
Subject index.