In just over 100 pages, this book provides basic, essential knowledge of some of the tools of real analysis: the Hardy-Littlewood maximal operator, the Calderon-Zygmund theory, the Littlewood-Paley theory, interpolation of spaces and operators, and the basics of H1 and BMO spaces. This concise text offers brief proofs and exercises of various ......
This volume contains the proceedings of the conference Representation Theory XVI, held from June 25-29, 2019, in Dubrovnik, Croatia. The articles in the volume address selected aspects of representation theory of reductive Lie groups and vertex algebras, and are written by prominent experts in the field as well as junior researchers. The three ......
Nonlinear algebra provides modern mathematical tools to address challenges arising in the sciences and engineering. It is useful everywhere, where polynomials appear: in particular, data and computational sciences, statistics, physics, optimization. The book offers an invitation to this broad and fast-developing area. It is not an extensive ......
Let $p$ be a prime and$S$ a finite $p$-group. A $p$-fusion system on $S$ is a category whose objects are the subgroups of $S$ and whose morphisms are certain injective group homomorphisms. Fusion systems are of interest in modular representation theory, algebraic topology, and local finite group theory. The book provides a characterization of the ......
From the Euclidean Space and the Circle to Lie Groups
Coordination, consensus, and synchronization are found in diverse natural phenomena and engineering applications. Examples are flocking birds, illuminating fireflies, a school of fish, and distributed control and sensing. The simplest of such problems are set in the Euclidean spaces and the circle. Consensus and Synchronization: From the Euclidean ......
The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to ......
Finite functions (in particular, Boolean functions) play a fundamental role in computer science and discrete mathematics. This work describes representations of Boolean functions that have small size for many important functions and which allow efficient work with the represented functions. The representation size of important and selected ......
This volume presents a fully self-contained introduction to the modular representation theory of the Iwahori-Hecke algebras of the symmetric groups and of the $q$-Schur algebras. The study of these algebras was pioneered by Dipper and James in a series of landmark papers. The primary goal of the book is to classify the blocks and the simple ......
