Due 2019-11-12
1st ed. 2019, XV, 285 p.
Printed book
Softcover
ISBN 978-3-030-28299-8
The simple tools described provide a new way of looking at group
representation theory and its applications
Offers an insight into the mind of one of the great mathematicians
Much of the work described has not previously appeared in book form
This book sets out an account of the tools which Frobenius used to discover representation
theory for nonabelian groups and describes its modern applications. It provides a new
viewpoint from which one can examine various aspects of representation theory and areas of
application, such as probability theory and harmonic analysis. For example, the focal objects of
this book, group matrices, can be thought of as a generalization of the circulant matrices which
are behind many important algorithms in information science. The book is designed to appeal
to several audiences, primarily mathematicians working either in group representation theory or
in areas of mathematics where representation theory is involved. Parts of it may be used to
introduce undergraduates to representation theory by studying the appealing pattern structure
of group matrices. It is also intended to attract readers who are curious about ideas close to
the heart of group representation theory, which do not usually appear in modern accounts, but
which offer new perspectives.
Due 2019-11-05
1st ed. 2019, 260 p. 17
illus., 2 illus. in color.
Printed book
Softcover
ISBN 978-981-32-9591-9
Introduces mathematically rigorous renormalisation group theory
Explores mathematically rigorous approaches
Based on the lecture notes for summer school courses
This is a primer on a mathematically rigorous renormalisation group theory, presenting
mathematical techniques fundamental to renormalisation group analysis such as Gaussian
integration, perturbative renormalisation and the stable manifold theorem. It also provides an
overview of fundamental models in statistical mechanics with critical behaviour, including the
Ising and 4models and the self-avoiding walk. The book begins with critical behaviour and its
basic discussion in statistical mechanics models, and subsequently explores perturbative and
non-perturbative analysis in the renormalisation group. Lastly it discusses the relation of these
topics to the self-avoiding walk and supersymmetry. Including exercises in each chapter to
help readers deepen their understanding, it is a valuable resource for mathematicians and
mathematical physicists wanting to learn renormalisation group theory
Due 2019-11-22
1st ed. 2019, XX, 480 p. 33
illus., 19 illus. in color.
Printed book
Softcover
ISBN 978-3-030-28534-0
Features contributions on state-of-the-art research in probability
Covers mainstream domains
Includes accessible presentations of classical results
This milestone 50th volume of the "Seminaire de Probabilites" pays tribute with a series of
memorial texts to one of its former editors, Jacques Azema, who passed away in January. The
founders of the "Seminaire de Strasbourg", which included Jacques Azema, probably had no
idea of thepossible longevity and success of theprocess they initiated in 1967. Continuing in
this long tradition, this volume contains contributions on state-of-art research on Brownian
filtrations, stochastic differential equations and their applications, regularity structures, quantum
diffusion,interlacing diffusions,mod-Oconvergence, Markov soup, stochastic billiards and other
current streams of research.
Due 2019-11-25
1st ed. 2019, XX, 280 p.
Printed book
Softcover
ISBN 978-3-030-29544-8
Presents advanced techniques for the KPZ equation and a wide bibliography
on singular SPDEs
IIncludes novel results for dispersive equations made possible by
randomizing initial conditions
Offers a unique exposition of the theory of fully nonlinear SPDEs
Written by leading experts in an emerging field, this book offers a unique view of the theory of
stochastic partial differential equations, with lectures on the stationary KPZ equation, fully
nonlinear SPDEs, and random data wave equations. This subject has recently attracted a great
deal of attention, partly as a consequence of Martin Hairer's contributions and in particular his
creation of a theory of regularity structures for SPDEs, for which he was awarded the Fields
Medal in 2014. The text comprises three lectures covering: the theory of stochastic Hamilton?
Jacobi equations, one of the most intriguing and rich new chapters of this subject; singular
SPDEs, which are at the cutting edge of innovation in the field following the breakthroughs of
regularity structures and related theories, with the KPZ equation as a central example; and the
study of dispersive equations with random initial conditions, which gives new insights into
classical problems and at the same time provides a surprising parallel to the theory of singular
SPDEs, viewed from many different perspectives. These notes are aimed at graduate students
and researchers who want to familiarize themselves with this new field, which lies at the
interface between analysis and probability
Due 2019-10-17
1st ed. 2019, XIX, 355 p. 6
illus.
Printed book
Softcover
ISBN 978-981-32-9740-1
Introduces jump processes for students who may not have had previous
experience with stochastic processes
Expedites understanding of the application of an infinite-dimensional
integration by parts formula for jump processe
Presents Levy processes in stages, with exercises to check the reader’s
progress
The present book deals with a streamlined presentation of Levy processes and their densities.
It is directed at advanced undergraduates who have already completed a basic probability
course. Poisson random variables, exponential random variables, and the introduction of
Poisson processes are presented first, followed by the introduction of Poisson random
measures in a simple case. With these tools the reader proceeds gradually to compound
Poisson processes, finite variation Levy processes and finally one-dimensional stable cases. This
step-by-step progression guides the reader into the construction and study of the properties of
general Levy processes with no Brownian component. In particular, in each case the
corresponding Poisson random measure, the corresponding stochastic integral, and the
corresponding stochastic differential equations (SDEs) are provided. The second part of the
book introduces the tools of the integration by parts formula for jump processes in basic
settings and first gradually provides the integration by parts formula in finite-dimensional
spaces and gives a formula in infinite dimensions. These are then applied to stochastic
differential equations in order to determine the existence and some properties of their
densities. As examples, instances of the calculations of the Greeks in financial models with
jumps are shown. The final chapter is devoted to the Boltzmann equation.
Due 2019-11-05
1st ed. 2019, X, 348 p. 28
illus., 9 illus. in color.
Printed book
Hardcover
ISBN 978-981-32-9300-7
Is the first comprehensive introduction of Mordell-Weil lattices that does
not
assume extensive prerequisites
Shows that the theory of Mordell-Weil lattices itself is very powerful
yet
relatively easy to master and apply
Demonstrates with many examples and applications how Mordell-Weil lattices
connect with several areas of mathematics
This book lays out the theory of Mordell-Weil lattices, a very powerful
and influential tool at
the crossroads of algebraic geometry and number theory, which offers many fruitful
connections to other areas of mathematics. The book presents all the ingredients entering into
the theory of Mordell-Weil lattices in detail, notably, relevant portions
of lattice theory, elliptic
curves, and algebraic surfaces. After defining Mordell-Weil lattices, the
authors provide several
applications in depth. They start with the classification of rational elliptic surfaces. Then a
useful connection with Galois representations is discussed. By developing the notion of
excellent families, the authors are able to design many Galois representations with given Galois
groups such as the Weyl groups of E6, E7 and E8. They also explain a connection to the
classical topic of the 27 lines on a cubic surface. Two chapters deal with elliptic K3 surfaces, a
pulsating area of recent research activity which highlights many central
properties of Mordell-
Weil lattices. Finally, the book turns to the rank problem-one of the key
motivations for the
introduction of Mordell-Weil lattices. The authors present the state of
the art of the rank
problem for elliptic curves both over Q and over C(t) and work out applications to the sphere
packing problem. Throughout, the book includes many instructive examples illustrating the
theory
Due 2019-11-23
1st ed. 2019, X, 110 p.
Printed book
Softcover
ISBN 978-3-030-26855-8
Provides an update on the current state of research in some key areas of
geometric representation theory and gauge theory
Features lectures authored by leading researchers in the area
Each lecture is self-contained
This book offers a review of the vibrant areas of geometric representation theory and gauge
theory, which are characterized by a merging of traditional techniques in representation theory
with the use of powerful tools from algebraic geometry, and with strong inputs from physics.
The notes are based on lectures delivered at the CIME school "Geometric Representation
Theory and Gauge Theory" held in Cetraro, Italy, in June 2018. They comprise three
contributions, due to Alexander Braverman and Michael Finkelberg, Andrei Negut, and Alexei
Oblomkov, respectively. Braverman and Finkelberg’s notes review the mathematical theory of
the Coulomb branch of 3D N=4 quantum gauge theories. The purpose of Negut’s notes is to
study moduli spaces of sheaves on a surface, as well as Hecke correspondences between
them. Oblomkov's notes concern matrix factorizations and knot homology. This book will appeal
to both mathematicians and theoretical physicists and will be a source of inspiration for PhD
students and researchers.
Due 2020-02-09
3rd ed. 2019, Approx. 610
p. 76 illus., 6 illus. in color.
Printed book
Hardcover
ISBN 978-3-030-29163-1
Presents a collection of methodologies formulated and developed in the
framework of linear models.
Offers accompanying R code online for the included analyses.
Features several new chapters, as well as new and expanded coverage in this 3rd edition.
Designed to be used independently or in conjunction with the theoretical
Plane Answers to Complex Questions.
Now in its third edition, this companion volume to Ronald Christensen’s PlaneAnswers to
Complex Questions uses three fundamental concepts from standard linear model theory?best
linear prediction, projections, and Mahalanobis distance? to extendstandard linear modeling
into the realms of Statistical Learning and Dependent Data. This new edition features a wealth
of new and revised content. In StatisticalLearning it delves into nonparametric regression,
penalized estimation (regularization),reproducing kernel Hilbert spaces, the kernel trick, and
support vector machines. For Dependent Data it uses linear model theory to examine general
linear models,linear mixed models, time series, spatial data, (generalized) multivariate
linearmodels, discrimination, and dimension reduction. While numerous references toPlane
Answers are made throughout the volume, Advanced Linear Modeling can be usedon its own
given a solid background in linear models. Accompanying R code for theanalyses is available
online.