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 ......
This book consists of a series of papers focusing on the mathematical and computational modeling and analysis of some real-life phenomena in the natural and engineering sciences. The book emphasizes three main themes: (i) the design and analysis of robust and dynamically-consistent nonstandard finite-difference methods for discretizing ......
This volume contains the proceedings of the AMS-EMS-SMF Special Session on Recent Advances in Diffeologies and Their Applications, held from July 18-20, 2022, at the Universite de Grenoble-Alpes, Grenoble, France. The articles present some developments of the theory of diffeologies applied in a broad range of topics, ranging from algebraic ......
Quantum algorithms are among the most important, interesting, and promising innovations in information and communication technology. They pose a major threat to today's cybersecurity and at the same time promise great benefits by potentially solving previously intractable computational problems with reasonable effort. The theory of quantum ......
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 ......
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 ......
We show that the generation problem in Thompson's group F is decidable, i.e., there is an algorithm which decides if a finite set of elements of F generates the whole F. The algorithm makes use of the Stallings 2-core of subgroups of F, which can be defined in an analogous way to the Stallings core of subgroups of a finitely generated free group. ......
Milliken's tree theorem is a deep result in combinatorics that generalizes a vast number of other results in the subject, most notably Ramsey's theorem and its many variants and consequences. In this sense, Milliken's tree theorem is paradigmatic of structural Ramsey theory, which seeks to identify the common combinatorial and logical features of ......
