Softcover ISBN: 978-1-4704-5673-3
Mathematical Surveys and Monographs Volume: 280
2024; 211 pp
Iwasawa theory began in the late 1950s with a series of papers by Kenkichi Iwasawa on ideal class groups in the cyclotomic tower of number fields and their relation to p
-adic L
-functions. The theory was later generalized by putting it in the context of elliptic curves and modular forms. The main motivation for writing this book was the need for a total perspective of Iwasawa theory that includes the new trends of generalized Iwasawa theory. Another motivation is to update the classical theory for class groups, taking into account the changed point of view on Iwasawa theory.
The goal of this second part of the three-part publication is to explain various aspects of the cyclotomic Iwasawa theory of p
-adic Galois representations.
Graduate students and researchers interested in number theory and arithmetic geometry.
Chapters
Introduction to cyclotomic Iwasawa theory of elliptic curves
Framework of cyclotomic Iwasawa theory for p
-adic Galois representations
Known results on cyclotomic Iwasawa theory for p
-adic representations
Appendix A
Softcover ISBN: 978-1-4704-7465-2
Mathematical Surveys and Monographs Volume: 281
2024; 342 pp
A fundamental question in the theory of discrete and continuous-time population models concerns the conditions for the extinction or persistence of populations ? a question that is addressed mathematically by persistence theory. For some time, it has been recognized that if the dynamics of a structured population are mathematically captured by continuous or discrete semiflows and if these semiflows have first-order approximations, the spectral radii of certain bounded linear positive operators (better known as basic reproduction numbers) act as thresholds between population extinction and persistence.
This book combines the theory of discrete-time dynamical systems with applications to population dynamics with an emphasis on spatial structure. The inclusion of two sexes that must mate to produce offspring leads to the study of operators that are (positively) homogeneous (of degree one) and order-preserving rather than linear and positive.
While this book offers an introduction to ordered normed vector spaces, some background in real and functional analysis (including some measure theory for a few chapters) will be helpful. The appendix and selected exercises provide a primer about basic concepts and about relevant topics one may not find in every analysis textbook.
Graduate students and researchers interested in the theory of discrete-time dynamical systems with applications in population dynamics.
Chapters
Introduction
Cones and ordered vector spaces
The ordered vector space of real measures
Homogeneous operators
Spectral radii for homogeneous operators
Order-bounded operators
Upper semicontinuity of spectral radii
A left resolvent for homogeneous operators
Eigenvectors of (pseudo-)compact homogeneous operators
Continuity of the spectral radius
Eigenfunctionals
Turnover versus reproduction number
Linear maps on the vector space of measures
Nonlinear dynamics
Unstructured population models
A rank-structured population with mating
Two diffusing sexes and short reproductive season
Nonlocal spatial spread of semelparous two-sex populations
Populations with measure-valued structural distributions
Appendix A. Some tools from real analysis
Softcover ISBN: 978-1-4704-7246-7
Contemporary Mathematics Volume: 799
2024; 215 pp
This volume contains the proceedings of the AMS Special Session on Recent Progress in Function Theory and Operator Theory, held virtually on April 6, 2022.
Function theory is a classical subject that examines the properties of individual elements in a function space, while operator theory usually deals with concrete operators acting on such spaces or other structured collections of functions. These topics occupy a central position in analysis, with important connections to partial differential equations, spectral theory, approximation theory, and several complex variables. With the aid of certain canonical representations or gmodelsh, the study of general operators can often be reduced to that of the operator of multiplication by one or several independent variables, acting on spaces of analytic functions or compressions of this operator to co-invariant subspaces. In this way, a detailed understanding of operators becomes connected with natural questions concerning analytic functions, such as zero sets, constructions of functions constrained by norms or interpolation, multiplicative structures granted by factorizations in spaces of analytic functions, and so forth. In many cases, non-obvious problems initially motivated by operator-theoretic considerations turn out to be interesting on their own, leading to unexpected challenges in function theory.
The research papers in this volume deal with the interplay between function
theory and operator theory and the way in which they influence each other
Graduate students and research mathematicians interested in functional analysis, complex analysis, and operator theory.
Articles
Pamela Gorkin and Elodie Pozzi ? Three open problems in function theoretic operator theory
Dmitry Khavinson, Erik Lundberg and Sean Perry ? On the valence of logharmonic polynomials
Michael R. Pilla ? A generalized cross ratio
Zhenghui Huo and Brett D. Wick ? Weighted estimates of the Bergman projection with matrix weights
Galia Dafni and Chun Ho Lau ? h1
boundedness of localized operators and commutators with bmo and lmo
Raymond Cheng and Christopher Felder ? On interpolation by functions in ?pA
Pierre-Olivier Parise ? Kernel-summability methods and the Silverman?Toeplitz Theorem
George Popescu and Gabriel T. Pr?jitur? ? On Rhaly operators on l2
William T. Ross ? The Cesaro operator
A co-publication of the AMS and Bar-Ilan University
Softcover ISBN: 978-1-4704-7555-0
Contemporary Mathematics, Volume: 800
Israel Mathematical Conference Proceedings
2024; 308 pp
This volume contains the proceedings of the Amitsur Centennial Symposium, held from November 1?4, 2021, virtually and at the Israel Institute for Advanced Studies (IIAS), The Hebrew University of Jerusalem, Jerusalem, Israel.
Shimshon Amitsur was a pioneer in several branches of algebra, the leading algebraist in Israel for several decades who contributed major theorems, inspiring results, useful observations, and enlightening tricks to many areas of the field.
The fifteen papers included in the volume represent the broad impact of Amitsur's work on such areas as the theory of finite simple groups, algebraic groups, PI-algebras and growth of rings, quadratic forms and division algebras, torsors and Severi-Brauer surfaces, Hopf algebras and braces, invariants, automorphisms and derivations.
Graduate students and research mathematicians interested in group theory, simple algebras, quadratic forms, representation theory, and ring theory.
Articles
Avinoam Mann ? Shimshon Avraham Amitsur (1921?1994)
Avinoam Mann ? Challenges for 21st century group theory
Levent Alpoge, Nicholas M. Katz, Gabriel Navarro, E. A. OfBrien and Pham Huu Tiep ? Local systems and Suzuki groups
Timothy C. Burness and Robert M. Guralnick ? On the generation of simple groups by Sylow subgroups
Miriam Cohen and Sara Westreich ? Representations of the quantum double of quasitriangular Hopf algebras
Adam Chapman and Anne Queguiner-Mathieu ? Minimal quadratic forms for the function field of a conic in characteristic 2
Uriya A. First ? Highly versal torsors
Beferi Greenfeld, Louis Rowen and Lance Small ? Optimal representability results of PI-algebras: nilpotency, growth and chain conditions
Daniel Krashen and Max Lieblich ? Transcendental splitting fields of division algebras
Michael Larsen and Aner Shalev ? Groups versus rings
Eliyahu Matzri ? On the symbol length of symbols
Oksana Bezushchak, Anatoliy Petravchuk and Efim Zelmanov ? Automorphisms and derivations of commutative and PI-algebras
Claudio Procesi ? Tensor fundamental theorems of invariant theory
Igor A. Rapinchuk ? Algebraic groups with good reduction and the genus problem
David J. Saltman ? Genus 1 curves in Severi?Brauer surfaces
Agata Smoktunowicz ? More on skew braces and their ideals
Softcover ISBN: 978-1-4704-7421-8
Pure and Applied Undergraduate Texts, Volume: 65
2024; 264 pp
An Introduction to Real Analysis gives students of mathematics and related sciences an introduction to the foundations of calculus, and more generally, to the analytic way of thinking. The authors' style is a mix of formal and informal, with the intent of illustrating the practice of analysis and emphasizing the process as much as the outcome.
The book is intended for use in a one- or two-term course for advanced undergraduates in mathematics and related fields who have completed two or three terms of a standard university calculus sequence.
Undergraduate students interested in a rigorous course in real analysis.
Chapters
The real numbers
Sequences and series
The topology of the real line
Continuous functions
Sequences and series of functions
Differentiation
The Riemann integral
The Lebesgue integral
Appendix A. Set theory and constructing R
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN: 978-1-4704-7678-6
Spectrum Volume 105
2024; 261 pp
This book is a charming collection of puzzles created by Yoshiyuki Kotani, one of the founding members of the Academy of Recreational Mathematics, Japan. Kotani has selected some of his favorite puzzles from over 40 years of puzzle setting, most of which have never appeared in western literature. The distinctive culture of Japanese recreational mathematics is encapsulated in this volume from one of its leading architects.
Beginning with a sampler of problems to whet the appetite, the reader is led through a three-course menu of combinatorial, arithmetic, and geometrical problems. Highlights include the Wagashi Combo, a puzzle devised during Kotani's youth, where the reader has to combine two plane figures to construct a new shape in two distinct ways. Everything is tied together with a playful narrative of a Japanese restaurant, adding fun and humor to the challenge. The book ends with a miscellany of problems that expand on the ideas from earlier chapters.
Suitable for anyone with an interest in recreational mathematics, the puzzles in this book require no formal mathematical training. Novice and experienced solvers alike will delight in this original and delicious offering of Japanese puzzles.
Undergraduate and graduate students and researchers interested in recreational mathematics/puzzles.
Appetizer / Scallop / Starter puzzles
A miscellany of puzzles
First course / Crab / Combinatorial puzzles
Combinatorial configurations
Chess puzzles
Information processing
Second course / Abalone / Arithmetical puzzles
Numerical configurations
Digital puzzles
Optimization puzzles
Third course / Lobster / Linear, planar & spatial puzzles
Polyomino puzzles
Dissection puzzles
Spatial & linear puzzles
Soup / Oyster / Other puzzles
The International Seafood Festival
Dessert / Prawn / Petite puzzles
Another miscellany of puzzles