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Stochastic Finance provides an introduction to mathematical finance that is unparalleled in its accessibility. Through classroom testing, the authors have identified common pain points for students, and their approach takes great care to help the reader to overcome...
Many researchers in geometric functional analysis are unaware of algebraic aspects of the subject and the advances they have permitted in the last half century. This book, written by two world experts on homological methods in Banach space theory, gives functional...
Bruhat–Tits theory is an important topic in number theory, representation theory, harmonic analysis, and algebraic geometry. This book gives the first comprehensive treatment of this theory over discretely valued Henselian fields. It can serve both as a reference for...
Discrete quantum walks are quantum analogues of classical random walks. They are an important tool in quantum computing and a number of algorithms can be viewed as discrete quantum walks, in particular Grover's search algorithm. These walks are constructed on an...
Rectifiable sets, measures, currents and varifolds are foundational concepts in geometric measure theory. The last four decades have seen the emergence of a wealth of connections between rectifiability and other areas of analysis and geometry, including deep links with...
Using the unifying notion of group actions, this second course in modern algebra introduces the deeper algebraic tools needed to get into topics only hinted at in a first course, like the successful classification of finite simple groups and how groups play a role in...
This up-to-date treatment of recent developments in geometric inverse problems introduces graduate students and researchers to an exciting area of research. With an emphasis on the two-dimensional case, topics covered include geodesic X-ray transforms, boundary...
This text on the theory and applications of network science is aimed at beginning graduate students in statistics, data science, computer science, machine learning, and mathematics, as well as advanced students in business, computational biology, physics, social...
Introducing foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, this text is based on Bastiani calculus. It focuses on two main areas of infinite-dimensional geometry: infinite-dimensional Lie groups and weak Riemannian geometry,...
During the past half-century, exponential families have attained a position at the center of parametric statistical inference. Theoretical advances have been matched, and more than matched, in the world of applications, where logistic regression by itself has become the...
Arithmetic groups are generalisations, to the setting of algebraic groups over a global field, of the subgroups of finite index in the general linear group with entries in the ring of integers of an algebraic number field. They are rich, diverse structures and they...
As a result of the COVID-19 pandemic, medical statistics and public health data have become staples of newsfeeds worldwide, with infection rates, deaths, case fatality and the mysterious R figure featuring regularly. However, we don't all have the statistical background...
In the middle of the last century, after hearing a talk of Mostow on one of his rigidity theorems, Borel conjectured in a letter to Serre a purely topological version of rigidity for aspherical manifolds (i.e. manifolds with contractible universal covers). The Borel...
Starting from where a first course in convex optimization leaves off, this text presents a unified analysis of first-order optimization methods – including parallel-distributed algorithms – through the abstraction of monotone operators. With the increased computational...
This new book on mathematical logic by Jeremy Avigad gives a thorough introduction to the fundamental results and methods of the subject from the syntactic point of view, emphasizing logic as the study of formal languages and systems and their proper use. Topics include...
This book proves some important new theorems in the theory of canonical inner models for large cardinal hypotheses, a topic of central importance in modern set theory. In particular, the author 'completes' the theory of Fine Structure and Iteration Trees (FSIT) by...
The analysis of eigenvalues of Laplace and Schrödinger operators is an important and classical topic in mathematical physics with many applications. This book presents a thorough introduction to the area, suitable for masters and graduate students, and includes an ample...
The goal of this monograph is to develop Hopf theory in the setting of a real reflection arrangement.The central notion is that of a Coxeter bialgebra which generalizes the classical notion of a connected graded Hopf algebra.The authors also introduce the more...
Since their introduction by Gromov in the 1980s, the study of bounded cohomology and simplicial volume has developed into an active field connected to geometry and group theory. This monograph, arising from a learning seminar for young researchers working in the area,...
Written in celebration of Miles Reid's 70th birthday, this illuminating volume contains 11 papers by leading mathematicians in and around algebraic geometry, broadly related to the themes and interests of Reid's varied career. Just as in Reid's own scientific output,...
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