This volume describes in monograph form important applications in numerical methods of linear algebra. The author presents material and extended results from recent papers in a readable style. The main goal of the book is to study the behaviour of the resolvent of a matrix under the perturbation by low rank matrices. Whereas the eigenvalues (the poles of the resolvent) and the pseudospectra (the sets where the resolvent takes large values) can move dramatically under such perturbations, the growth of the resolvent as a matrix-valued meromorphic function remains essentially unchanged. This has...
This volume describes in monograph form important applications in numerical methods of linear algebra. The author presents material and extended resul...
Discusses the connection between Calabi-Yau threefolds and modular forms. This title presents the general theory and brings together the known results. It features hundreds of examples of rigid and non-rigid Calabi-Yau threefolds, and the construction of c
Discusses the connection between Calabi-Yau threefolds and modular forms. This title presents the general theory and brings together the known results...
A monograph that is concerned with Galois theoretical embedding problems of so-called Brauer type with a focus on 2-groups and on finding explicit criteria for solvability and explicit constructions of the solutions. It also considers questions of reducing
A monograph that is concerned with Galois theoretical embedding problems of so-called Brauer type with a focus on 2-groups and on finding explicit cri...
This is a timely introduction to an intensively studied topic of conformal field theory with gauge symmetry by a leading algebraic geometer, and includes all the necessary techniques and results that are used to construct the modular functor.
This is a timely introduction to an intensively studied topic of conformal field theory with gauge symmetry by a leading algebraic geometer, and inclu...
This book resulted from the lectures held at The Fields Institute (Waterloo, ON, Canada). Leading international experts presented current results on the theory of C*-algebras and von Neumann algebras, together with recent work on the classification of C*-algebras. Much of the material in the book is appearing here for the first time and is not available elsewhere in the literature.
This book resulted from the lectures held at The Fields Institute (Waterloo, ON, Canada). Leading international experts presented current results on t...
This book collects some recent developments in stochastic control theory with applications to financial mathematics. We first address standard stochastic control problems from the viewpoint of the recently developed weak dynamic programming principle. A special emphasis is put on the regularity issues and, in particular, on the behavior of the value function near the boundary. We then provide a quick review of the main tools from viscosity solutions which allow to overcome all regularity problems. We next address the class of stochastic target problems which extends in a nontrivial way...
This book collects some recent developments in stochastic control theory with applications to financial mathematics. We first address standard ...
Inner functions form an important subclass of bounded analytic functions. Since they have unimodular boundary values, they appear in many extremal problems of complex analysis. They have been extensively studied since early last century, and the literature on this topic is vast. Therefore, this book is devoted to a concise study of derivatives of these objects, and confined to treating the integral means of derivatives and presenting a comprehensive list of results on Hardy and Bergman means. The goal is to provide rapid access to the frontiers of research in this field. This monograph will...
Inner functions form an important subclass of bounded analytic functions. Since they have unimodular boundary values, they appear in many extremal pro...
This book addresses the need for an accessible comprehensive exposition of the theory of uniform measures; the need that became more critical when recently uniform measures reemerged in new results in abstract harmonic analysis. Until now, results about uniform measures have been scattered through many papers written by a number of authors, some unpublished, written using a variety of definitions and notations. Uniform measures are certain functionals on the space of bounded uniformly continuous functions on a uniform space. They are a common generalization of several classes of...
This book addresses the need for an accessible comprehensive exposition of the theory of uniform measures; the need that became more critical w...
This monograph gives a short introduction to the relevant modern parts of discrete geometry, in addition to leading the reader to the frontiers of geometric research on sphere arrangements. The readership is aimed at advanced undergraduate and early graduate students, as well as interested researchers. It contains more than 40 open research problems ideal for graduate students and researchers in mathematics and computer science. Additionally, this book may be considered ideal for a one-semester advanced undergraduate or graduate level course.
The core part of this book is...
This monograph gives a short introduction to the relevant modern parts of discrete geometry, in addition to leading the reader to the frontiers of ...
This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the current open problems. Affine Schubert calculus lies at the crossroads of combinatorics, geometry, and representation theory. Its modern development is motivated by two seemingly unrelated directions. One is the introduction of k-Schur functions in the study of Macdonald polynomial positivity, a mostly combinatorial branch of symmetric function theory. The other direction is the study of the Schubert bases of the (co)homology of the...
This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and s...
