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MSJ MemoirsMathematical Society of Japan |
| Editorial Board | |||||
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S. Naito(Editor-in-chief, Tokyo Tech) H. Endo(Managing Editor, Tokyo Tech) G. Akagi(Tohoku), A. Atsuji(Keio), K. Bannai(Keio), H. Endo(Tokyo Tech), O. Fujino(Kyoto), T. Itoh(Kyoto), J. Kamimoto(Kyushu), M. Kanai(Tokyo), K. Kato(TUS), M. Kubo(Nagoya), H. Masuda(Kyushu), S. Naito(Tokyo Tech), M. Okado(Osaka City), S. Seirin-Lee(Hiroshima), T. Shioya(Tohoku), K. Takemura(Ochanomizu), K. Yokoyama(Rikkyo) |
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The series MSJ Memoirs is devoted to the publications of
lecture notes, graduate textbooks and long research papers* in
pure and applied mathematics. In principle, two to three volumes
are published each year by the Mathematical Society of Japan.
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| Submission: Each volume should be an integrated monograph. Proceedings of conferences or collections of independent papers are not accepted. The author(s) can submit the article to one of the editors in the form of hard copy. When the article is accepted, the author(s) is (are) requested to send a camera-ready manuscript. For further technical conditions, please contact one of the editors. | |||||
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Subscription/Orders: Each volume can be purchased separately.
Orders from inside Japan can be made directly to the Mathematical Society of Japan. From Volume 15 onward, the distribution of the series outside Japan is conducted exclusively through World Scientific Publishing Company. For details, see the website:
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| List of Titles | ||
| Vol.40 | Author: | Yuji Odaka and Yoshiki Oshima |
| Title: | Collapsing K3 Surfaces, Tropical Geometry and Moduli Compactifications of Satake, Morgan-Shalen Type | |
|
This research monograph mainly discusses a canonical and explicit
compactification of the moduli spaces of abelian varieties, K3 surfaces
and compact hyperKähler varieties. For that, we use two theories of
compactification---Satake compactifications for locally symmetric spaces
in terms of the Lie theory, and Morgan-Shalen compactifications of
complex varieties in terms of valuations. We show they coincide for
Shimura varieties. The obtained compactifications are no longer
varieties but we provide geometric meanings to them. We partially prove that the boundary parametrizes collapsed limits of the Ricci-flat Kähler metrics. Such limits also coincide with a posteriori defined “tropicalized version” or equivalently the dual graphs of degenerations of original varieties. From differential geometric perspective, this work provides a moduli-theoretic framework for the limiting behavior of Ricci-flat Kähler metrics. From Lie theoretic perspective, this work provides a geometric meaning to the Satake compactification associated to adjoint representations, which are not the same as the Baily-Borel compactifications. Applying our theory to the case of one parameter maximal degeneration of K3 surfaces, we obtain proofs of conjectures of Gross-Wilson and Kontsevich-Soibelman. We formulate general conjectures on the limits of Ricci-flat Kähler metrics in the above framework and partially prove them, but they largely remain open. 2021, 165p, ISBN: 978-4-86497-104-1 | ||
| Vol.39 | Author: | Masaharu Taniguchi |
| Title: | Traveling Front Solutions in Reaction-Diffusion Equations | |
|
The study on traveling fronts in reaction-diffusion equations is the
first step to understand various kinds of propagation phenomena in
reaction-diffusion models in natural science. One dimensional traveling
fronts have been studied from the 1970s, and multidimensional ones have
been studied from around 2005. This volume is a text book for graduate
students to start their studies on traveling fronts. Using the phase
plane analysis, we study the existence of traveling fronts in several
kinds of reaction-diffusion equations. For a nonlinear reaction term, a
bistable one is a typical one. For a bistable reaction-diffusion
equation, we study the existence and stability of two-dimensional V-form
fronts, and we also study pyramidal traveling fronts in three or higher
space dimensions. The cross section of a pyramidal traveling front forms
a convex polygon. It is known that the limit of a pyramidal traveling
front gives a new multidimensional traveling front. For the study the
multidimensional traveling front, studying properties of pyramidal
traveling fronts plays an important role. In this volume, we study the
existence, uniqueness and stability of a pyramidal traveling front as
clearly as possible for further studies by graduate students.
For a help of their studies, we briefly explain and prove the
well-posedness of reaction-diffusion equations and the Schauder
estimates and the maximum principles of solutions.
2021, 170p, ISBN: 978-4-86497-097-6 | ||
| Vol.38 | Author: | Alex Casella, Dominic Tate and Stephan Tillmann |
| Title: | Moduli spaces of real projective structures on surfaces | |
|
This book is an excellent first encounter with the burgeoning field
of real projective manifolds. It gives a comprehensive introduction to
the theory of real projective structures on surfaces and their moduli
spaces. A central theme is an attractive parameterisation of moduli
space discovered by Fock and Goncharov that allows the explicit
description or analysis of many key features. These include a natural
Poisson structure, the effect of projective duality, holonomy
representations and the geometry of ends, to name but a few.
This book is written with two kinds of readers in mind: those who would like to learn about real projective surfaces or manifolds, and those who have a passing knowledge thereof but are interested in the geometric underpinnings of Fock and Goncharov’s parameterisation of moduli space of certain real projective structures. The material is accessible to any mathematician interested in these topics. It is presented in a self-contained manner with minimal prerequisites. Applications of Fock and Goncharov’s parameterisation of moduli space presented in this book include new proofs of results by Teichmüller (1939) concerning hyperbolic structures, by Goldman (1990) concerning closed surfaces, and by Marquis (2010) concerning structures of finite area. 2020, 122p, ISBN: 978-4-86497-096-9 | ||
| Vol.37 | Author: | Kazuki Hiroe, Hiroshi Kawakami, Akane Nakamura and Hidetaka Sakai |
| Title: | 4-dimensional Painlevé-type equations | |
|
The Painlevé equations were discovered as nonlinear ordinary
differential equations that define new special functions, and their
importance has long been recognized. Since the 1990s, there have been
many studies on various generalizations of the Painlevé equations such
as discretizations, higher dimensional analogues, quantizations, and so
on. The aim of this book is to provide a unified approach to understand
higher dimensional analogues of the Painlevé equations from the
viewpoint of the deformation theory of linear ordinary differential
equations. Especially, a detailed study will be given when the phase
spaces of their Hamiltonian systems are four dimensional. More
specifically, starting from the classification of the Fuchsian equations
with four accessory parameters, we construct a degeneration scheme of
linear equations by considering confluences of singular points. Then we
write down the Hamiltonians of the Painlevé-type equations associated
with these resulting linear equations. The following topics are
explained together with examples: spectral types of linear equations, a
method to calculate the Hamiltonians, confluences of singularities and
degenerations of the Painlevé-type equations, the correspondence between
linear equations or their spectral types through the Laplace transform.
In addition, Appendix 1 discusses symmetries of moduli spaces of linear
equations. As its application, it is shown that the equations obtained
in this book constitute a complete list of 4-dimensional Painlevé-type
equations corresponding to unramified linear equations. Appendix 2 gives
a list of the 4-dimensional Painlevé-type equations corresponding to
ramified linear equations.
2018, 172p, ISBN: 978-4-86497-087-7 | ||
| Vol.36 | Author: | Soichiro Katayama |
| Title: | Global solutions and the asymptotic behavior for nonlinear wave equations with small initial data | |
|
In the study of the Cauchy problem for nonlinear wave equations with
small initial data, the case where the nonlinearity has the critical
power is of special interest. In this case, depending on the structure
of the nonlinearity, one may observe global existence and finite time
blow-up of solutions. In 80’s, Klainerman introduced a sufficient
condition, called the null condition, for the small data global
existence in the critical case. Recently, weaker sufficient conditions
are also studied. This volume offers a comprehensive survey of the theory of nonlinear wave equations, including the classical local existence theorem, the global existence in the supercritical case, the finite time blow-up and the lifespan estimate in the critical case, and the global existence under the null condition in two and three space dimensions. The main tool here is the so-called vector field method. This volume also contains recent progress in the small data global existence under some conditions weaker than the null condition, and it is shown that a wide variety of the asymptotic behavior is observed under such weaker conditions. This volume is written not only for researchers, but also for graduate students who are interested in nonlinear wave equations. The exposition is intended to be self-contained and a complete proof is given for each theorem. 2017, 298p, ISBN: 978-4-86497-054-9 | ||
| Vol.35 | Author: | Osamu Fujino |
| Title: | Foundations of the minimal model program | |
|
Around 1980, Shigefumi Mori initiated a new theory, which
is now known as the minimal model program or Mori theory,
for higher-dimensional algebraic varieties. This theory has
developed into a powerful tool with applications to diverse
questions in algebraic geometry and related fields. One of the main purposes of this book is to establish the fundamental theorems of the minimal model program, that is, various Kodaira type vanishing theorems, the cone and contraction theorem, and so on, for quasi-log schemes. The notion of quasi-log schemes was introduced by Florin Ambro and is now indispensable for the study of semi-log canonical pairs from the cohomological point of view. By the recent developments of the minimal model program, we know that the appropriate singularities to permit on the varieties at the boundaries of moduli spaces are semi-log canonical. In order to achieve this goal, we generalize Kollár's injectivity, torsion-free, and vanishing theorems for reducible varieties by using the theory of mixed Hodge structures on cohomology with compact support. We also review many important classical Kodaira type vanishing theorems in detail and explain the basic results of the minimal model program for the reader's convenience. 2017, 289p, ISBN: 978-4-86497-045-7 | ||
| Vol.34 | Author: | Martin T. Barlow, Tibor Jordán and Andrzej Zuk |
| Title: | Discrete Geometric Analysis | |
|
This is a volume of lecture notes based on three series of lectures given by visiting professors of RIMS,
Kyoto University during the year-long project "Discrete Geometric Analysis", which took place in the
Japanese academic year 2012-13. The aim of the project was to make comprehensive research on topics
related to discreteness in geometry, analysis and optimization. Discrete geometric analysis is a hybrid field of several traditional disciplines, including graph theory, geometry, discrete group theory, and probability. The name of the area was coined by Toshikazu Sunada, and since being introduced, it has been extending and making new interactions with many other fields. This volume consists of three chapters: (I) Loop Erased Walks and Uniform Spanning Trees, by Martin T. Barlow. (II) Combinatorial Rigidity: Graphs and Matroids in the Theory of Rigid Frameworks, by Tibor Jordán. (III) Analysis and Geometry on Groups, by Andrzej Zuk. The lecture notes are useful surveys that provide an introduction to the history and recent progress in the areas covered. They will also help researchers who work in related interdisciplinary fields to gain an understanding of the material from the viewpoint of discrete geometric analysis. 2016, 157p, ISBN: 978-4-86497-035-8 | ||
| Vol.33 | Author: | Masaki Maruyama with collaboration of T. Abe and M. Inaba |
| Title: |
Moduli spaces of stable sheaves on schemes restriction theorems, boundedness and the GIT construction |
|
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The notion of stability for algebraic vector bundles on curves was originally introduced by Mumford, and moduli spaces of semi-stable vector bundles were studied intensively by Indian mathematicians. The notion of stability for algebraic sheaves was generalized to higher dimensional varieties. The study of moduli spaces of algebraic sheaves not only on curves but also on higher dimensional algebraic varieties has attracted much interest for decades and its importance has been increasing not only in algebraic geometry but also in related fields as differential geometry, mathematical physics. Masaki Maruyama is one of the pioneers in the theory of algebraic vector bundles on higher dimensional algebraic varieties. This book is a posthumous publication of his manuscript. It starts with basic concepts such as stability of sheaves, Harder-Narasimhan filtration and generalities on boundedness of sheaves. It then presents fundamental theorems on semi-stable sheaves : restriction theorems of semi-stable sheaves, boundedness of semi-stable sheaves, tensor products of semi-stable sheaves. Finally, after constructing quote-schemes, it explains the construction of the moduli space of semi-stable sheaves. The theorems are stated in a general setting and the proofs are rigorous. 2016, 154p, ISBN: 978-4-86497-034-1 | ||
| Vol.32 | Author: | Hiroshi Isozaki and Yaroslav Kurylev |
| Title: | Introduction to spectral theory and inverse problem on asymptotically hyperbolic manifolds | |
|
This manuscript is devoted to a rigorous and detailed exposition of the spectral theory and associated forward and inverse
scattering problems for the Laplace-Beltrami operators on asymptotically hyperbolic manifolds. Based upon the
classical stationary scattering theory in $\mathbb{R}^n$, the key point of the approach is the generalized Fourier transform, which serves as the basic tool to introduce and analyse the time-dependent wave
operators and the $S$-matrix. The crucial role is played by the characterization of the space of the
scattering solutions for the Helmholtz equations utilizing a properly defined Besov-type space. After developing the scattering theory, we describe, for some cases, the inverse scattering on the asymptotically hyperbolic manifolds by adopting, for the considered case, the boundary control method for inverse problems. The manuscript is aimed at graduate students and young mathematicians interested in spectral and scattering theories, analysis on hyperbolic manifolds and theory of inverse problems. We try to make it self-consistent and, to a large extent, not dependent on the existing treatises on these topics. To our best knowledge, it is the first comprehensive description of these theories in the context of the asymptotically hyperbolic manifolds. 2014, 251p, ISBN: 978-4-86497-021-1 | ||
| Vol.31 | Author: | Satoshi Takanobu |
| Title: | Bohr-Jessen Limit Theorem, Revisited | |
|
This book is a self-contained exposition on the Bohr-Jessen
limit theorem. This limit theorem, which is concerned with the
behavior of the Riemann zeta function $\zeta(s)$ on the line $
\mathrm{Re}\,s = \sigma$, where $1/2 < \sigma \leq 1$, was
found by Bohr-Jessen in the early 1930s. After Bohr-Jessen,
alternative proofs were given by Jessen-Wintner,
Borchsenius-Jessen, Laurinčikas, Matsumoto and others.
They dealt with this within the framework of probability
theory. Their formulation, originated by Jessen-Wintner, is
standard nowadays. The present book proposes a new approach for
the formulation to refine their works. By this method, the
whole story of the proof of the Bohr-Jessen limit theorem will
now become clearer, so that the reader must be able to
understand the essence of the proof in depth but without
difficulty.
2013, 216p, ISBN: 978-4-86497-019-8 | ||
| Vol.30 | Author: | Tatsuo Nishitani |
| Title: | Cauchy Problem for Noneffectively Hyperbolic Operators | |
|
At a double characteristic point of a differential operator
with real characteristics, the linearization of the Hamilton
vector field of the principal symbol is called the Hamilton
map and according to either the Hamilton map has non-zero real
eigenvalues or not, the operator is said to be effectively
hyperbolic or noneffectively hyperbolic.
For noneffectively hyperbolic operators, it was proved in the late of 1970s that for the Cauchy problem to be $C^{\infty}$ well posed the subprincipal symbol has to be real and bounded, in modulus, by the sum of modulus of pure imaginary eigenvalues of the Hamilton map. It has been recognized that what is crucial to the $C^{\infty}$ well-posedness is not only the Hamilton map but also the behavior of orbits of the Hamilton flow near the double characteristic manifold and the Hamilton map itself is not enough to determine completely the behavior of orbits of the flow. Strikingly enough, if there is an orbit of the Hamilton flow which lands tangentially on the double characteristic manifold then the Cauchy problem is not $C^{\infty}$ well posed even though the Levi condition is satisfied, only well posed in much smaller function spaces, the Gevrey class of order $1\leq s<5$ and not well posed in the Gevrey class of order $s>5$. In this lecture, we provide a general picture of the Cauchy problem for noneffectively hyperbolic operators, from the view point that the Hamilton map and the geometry of orbits of the Hamilton flow completely characterizes the well/not well-posedness of the Cauchy problem, exposing well/not well-posed results of the Cauchy problem with detailed proofs. 2013, 170p, ISBN: 978-4-86497-018-1 | ||
| Vol.29 | Author: | Takeshi Hirai, Akihito Hora and Etsuko Hirai |
| Title: | Projective representations and spin characters of complex reflection groups $G(m, p, n)$ and $G(m, p, \infty)$ | |
|
This volume consists of one expository paper and two research papers:
1.
T. Hirai, A. Hora and E. Hirai,
Introductory expositions on projective representations of
groups (referred as [E]);
2.
T. Hirai, E. Hirai and A. Hora,
Projective representations and spin characters of
complex reflection groups $G(m,p,n)$ and $G(m,p,\infty)$, I;
3.
T. Hirai, A. Hora and E. Hirai,
Projective representations and spin characters of
complex reflection groups $G(m,p,n)$ and $G(m,p,\infty)$, II,
Case of generalized symmetric groups.
Since Schur's trilogy on 1904 and so on, many mathematicians studied projective representations of groups and algebras, and also of their characters. Nevertheless, to invite mathematicians to this interesting and important areas, the paper [E] collects introductory expositions, with a historical plotting, for the theory of projective representations of groups and their characters. The paper [I] treats general theory for projective (or spin) representations and spin characters of complex reflection groups $G(m,p,n)$ and $G(m,p,\infty)=\lim_{n\to\infty}G(m,p,n)$, and clarifies the intimate relations between mother groups, $G(m,1,n)$, $G(m,1,\infty) (p=1)$, called generalized symmetric groups, and their child groups, $G(m,p,n)$, $G(m,p,\infty) (p|m, p>1)$. Also we treat explicitly a case of spin type in connection with the case of non-spin type (i.e. of linear representations). A detailed and general account on the so-called Vershik-Kerov theory on limits of characters is added. The paper [II] treats spin irreducible representations and spin characters of generalized symmetric groups (mother groups) for other spin types. 2013, 272p, ISBN: 978-4-86497-017-4 | ||
| Vol.28 | Author: | Toshio Oshima |
| Title: | Fractional calculus of Weyl algebra and Fuchsian differential equations | |
|
In this book we give a unified interpretation of confluences,
contiguity relations and Katz's middle convolutions for linear
ordinary differential equations with polynomial coefficients and
their generalization to partial differential equations.
The integral representations and series expansions of their
solutions are also within our interpretation.
As an application to Fuchsian differential equations on
the Riemann sphere, we construct a universal model of
Fuchsian differential equations with a given spectral type,
in particular, we construct a single ordinary differential
equation without apparent singularities corresponding to
any rigid local system on the Riemann sphere, whose existence
was an open problem presented by N. Katz.
Furthermore we obtain fundamental properties of the solutions of
the rigid Fuchsian differential equations such as their
connection coefficients and the necessary and sufficient
condition for the irreducibility of their monodromy groups.
We give many examples calculated by our fractional calculus.
2012, 203p, ISBN: 978-4-86497-016-7 | ||
| Vol.27 | Author: | Suhyoung Choi |
| Title: | Geometric Structures on 2-Orbifolds: Exploration of Discrete Symmetry | |
|
This book exposes the connection between the low-dimensional orbifold
theory and geometry that was first discovered by Thurston in
1970s providing a key tool in his proof of the hyperbolization of Haken
3-manifolds. Our main aims are to explain most of the topology of
orbifolds but to explain the geometric structure theory only for
2-dimensional orbifolds, including their Teichmüller (Fricke) spaces. We
tried to collect the theory of orbifolds scattered in various literatures
for our purposes. Here, we set out to write down the traditional approach
to orbifolds using charts, and we include the categorical definition
using groupoids. We will also maintain a collection of illustrative
MathematicaTM packages at our homepages. 2012, 182p, ISBN: 978-4-931469-68-6 | ||
| Vol.26 | Author: | Shinya Nishibata and Masahiro Suzuki |
| Title: | Hierarchy of semiconductor equations: relaxation limits with initial layers for large initial data | |
|
This volume provides a recent study of mathematical research
on semiconductor equations.
With recent developments in semiconductor technology,
several mathematical models have been established to analyze
and to simulate the behavior of electron flow in semiconductor devices.
Among them, a hydrodynamic, an energy-transport and a drift-diffusion models are
frequently used for the device simulation with the suitable choice,
depending on the purpose of the device usage.
Hence, it is interesting and important not only in mathematics but also in engineering
to study a model hierarchy, relations among these models.
The model hierarchy has been formally understood by relaxation limits
letting the physical parameters, called relaxation times, tend to zero.
The main concern of this volume is
the mathematical justification of the relaxation limits.
Precisely, we show that the time global solution for the hydrodynamic model
converges to that for the energy-transport model as a momentum relaxation time tends to zero.
Moreover, it is shown that the solution for the energy-transport model converges to
that for the drift-diffusion model as an energy relaxation time tends to zero.
For beginners' help, this volume also presents
the physical background of the semiconductor devices,
the derivation of the models,
and the basic mathematical results such as
the unique existence of time local solutions.
2011, 109p, ISBN: 978-4-931469-66-2 | ||
| Vol.25 | Author: | Hiroshi Sugita |
| Title: | Monte Carlo method, random number, and pseudorandom number | |
|
Although the Monte Carlo method is used in so many fields, its
mathematical foundation has been weak until now because of the
fundamental problem that a computer cannot generate random numbers.
This book presents a strong mathematical formulation of the Monte
Carlo method which is based on the theory of random number by
Kolmogorov and others and that of pseudorandom number by Blum and
others. As a result, we see that the Monte Carlo method may not need
random numbers and pseudorandom numbers may suffice. In particular,
for the Monte Carlo integration, there exist pseudorandom numbers
which serve as complete substitutes for random numbers.
2011, 133p, ISBN: 978-4-931469-65-5 | ||
| Vol.24 | Author: | Taro Asuke |
| Title: | Godbillon-Vey class of transversely holomorphic foliations | |
|
This volume provides a study of the Godbillon-Vey class and other real secondary characteristic classes of transversely holomorphic foliations.
One of the main tools in the study is complex secondary characteristic classes.
Intended to be self-contained and introductory, this volume contains a brief survey of the theory of secondary characteristic classes of transversely holomorphic foliations.
A construction of secondary characteristic classes of families of such foliations is also included.
By means of these classes, new proofs of the rigidity of the Godbillon-Vey class in the category of transversely holomorphic foliations are given.
2010, 130p, ISBN: 978-4-931469-61-7 | ||
| Vol.23 | Author: | Armen Sergeev |
| Title: | Kähler geometry of loop spaces | |
|
In this book we study three important classes of
infinite-dimensional Kähler manifolds --- loop
spaces of compact Lie groups, Teichmüller spaces of complex
structures on loop spaces, and Grassmannians of Hilbert spaces.
Each of these manifolds has a rich Kähler geometry, considered
in the first part of the book, and may be considered
as a universal object in a category, containing all its
finite-dimensional counterparts. On the other hand, these manifolds are closely related to string theory. This motivates our interest in their geometric quantization presented in the second part of the book together with a brief survey of geometric quantization of finite-dimensional Kähler manifolds. The book is provided with an introductory chapter containing basic notions on infinite-dimensional Frechet manifolds and Frechet Lie groups. It can also serve as an accessible introduction to Kähler geometry of infinite-dimensional complex manifolds with special attention to the aforementioned three particular classes. It may be interesting for mathematicians working with infinite-dimensional complex manifolds and physicists dealing with string theory. 2010, 212p, ISBN: 978-4-931469-60-0 | ||
| Vol.22 | Author: | Michael Ruzhansky and James Smith |
| Title: | Dispersive and Strichartz estimates for hyperbolic equations with constant coefficients | |
|
In this work dispersive and Strichartz estimates for solutions to
general strictly hyperbolic partial differential equations with
constant coefficients with lower order terms are considered.
The global time decay estimates of $L^p-L^q$ norms of propagators
are analysed in detail and it is described how the time decay rates
depend on the geometry of the problem. For these purposes,
the frequency space is separated in several zones each
giving a certain decay rate. Geometric conditions on
characteristics responsible for the particular decay
are presented. A comprehensive analysis is carried out for strictly hyperbolic equations of high orders with lower order terms of a general form. Most of the analysis also applies to equations with are pseudo-differential in the space variables. We also show how the obtained estimates apply to solutions to hyperbolic systems with constant coefficients. The applications of the obtained results include the time decay estimates for the solutions to the Fokker-Planck equation and for the solutions of semilinear hyperbolic equations. 2010, 147p, ISBN: 978-4-931469-57-0 | ||
| Vol.21 | Author: | Gautami Bhowmik, Kohji Matsumoto and Hirofumi Tsumura (Eds.) |
| Title: | Algebraic and Analytic Aspects of Zeta Functions and $L$-functions | |
|
This volume contains lectures presented at the
French-Japanese Winter School on Zeta and $L$-functions,
held at Muira, Japan, 2008.
The main aim of the School was to study various aspects of zeta
and $L$-functions with special emphasis on recent developments.
A series of detailed lectures were given by experts in topics
that include height zeta-functions, spherical
functions and Igusa zeta-functions, multiple zeta values and
multiple zeta-functions, classes of Euler products of zeta-functions,
and $L$-functions associated with modular forms.
This volume should be helpful to future generations in their
study of the fascinating theory of zeta and $L$-functions.
2010, 183p, ISBN: 978-4-931469-56-3 | ||
| Vol.20 | Author: | Danny Calegari |
| Title: | scl | |
|
This book is a comprehensive introduction to the theory of stable commutator length, an important subfield of quantitative topology, with substantial connections to 2-manifolds, dynamics, geometric group theory, bouded cohomology, symplectic topology, and many other subjects. We use constructive methods whenever possible, and focus on fundamental and explicit examples. We give a self-contained presentation of several foundational results in the theory, including Bavard's Duality Theorem, the Spectral Gap Theorem, the Rationality Theorem, and the Central Limit Theorem. The contents should be accessible to any mathematician interested in these subjects, and are presented with a minimal number of prerequisites, but with a view to applications in many areas of mathematics.
2009, 217p, ISBN: 978-4-931469-53-2 | ||
| Vol.19 | Author: | Joseph Najnudel, Bernard Roynette and Marc Yor |
| Title: | A Global View of Brownian Penalisations | |
|
The present volume is an expository monograph
on Brownian penalisation, an important new notion
the authors introduced to the theory of Wiener measure
and Markov processes. It will serve as a concise guidebook
for students and researchers who study probability theory,
stochastic processes and mathematical finance. 2009, 137p, ISBN: 978-4-931469-52-5 | ||
| Vol.18 | Author: | Yasutaka Ihara |
| Title: | On Congruence Monodromy Problems | |
|
It is now well-known that the group $SL_2(\mathbf{Z}[\frac{1}{p}])$ and the system of modular curves over $\mathbf{F}_{p^2}$ are ``closely related", and that the latter provided first ``examples" of curves over finite fields having many rational points. However, the ``three basic relationships", which really justify the former to be called the arithmetic fundamental group of the latter, still do not seem to be so commonly known. This book consists of two parts; a reproduction of the author's unpublished Lecture Notes (1968,69), and Author's Notes (2008). The former starts with explicit three main conjectural relationships for more general cases and gives various approaches towards their proofs. Though remained formally unpublished, these Lecture Notes had been widely circulated and have stimulated researches in various directions. The main conjectures themselves have also been proved since then. The Author's Notes (2008) gives detailed explanations of these developments, together with open problems. 2008, 230p, ISBN: 978-4-931469-50-1 | ||
| Vol.17 | Author: | Arkady Berenstein, David Kazhdan, Cédric Lecouvey, Masato Okado, Anne Schilling, Taichiro Takagi and Alexander Veselov |
| Title: | Combinatorial Aspect of Integrable Systems | |
|
This volume is a collection of six papers based on
the expository lectures of the workshop
``Combinatorial Aspect of Integrable Systems" held at RIMS
during July 26--30, 2004, as a part of the Project Research 2004
``Method of Algebraic Analysis in Integrable Systems". The topics range over crystal bases of quantum groups, its algebro-geometric analogue known as geometric crystal, generalizations of Robinson-Schensted type correspondence, fermionic formula related to Bethe ansatz, applications of crystal bases to soliton celluar automata, Yang-Baxter maps, and integrable discrete dynamics. All the papers are friendly written with many illustrative examples and intimately related to each other. This volume will serve as a good guide for researchers and graduate students who are interested in this fascinating subject. 2007, 167p, ISBN: 978-4-931469-37-2 | ||
| Vol.16 | Author: | Brian H. Bowditch |
| Title: | A course on geometric group theory | |
|
This volume is intended as a self-contained introduction
to the basic notions of geometric group theory,
the main ideas being illustrated with various examples and
exercises. One goal is to establish the foundations of the theory of
hyperbolic groups. There is a brief discussion of classical hyperbolic geometry, with a view to motivating and illustrating this. The notes are based on a course given by the author at the Tokyo Institute of Technology, intended for fourth year undergraduates and graduate students, and could form the basis of a similar course elsewhere. Many references to more sophisticated material are given, and the work concludes with a discussion of various areas of recent and current research. 2006, 104p, ISBN: 4-931469-35-3 | ||
| Vol.15 | Author: | Valery Alexeev and Viacheslav V. Nikulin |
| Title: | Del Pezzo and K3 surfaces | |
|
The present volume is a self-contained exposition on the complete
classification of singular del Pezzo surfaces of index one or two.
The method of the classification used here depends on the intriguing
interplay between del Pezzo surfaces and K3 surfaces, between geometry
of exceptional divisors and the theory of hyperbolic lattices. The topics involved contain hot issues of research in algebraic geometry, group theory and mathematical physics. This book, written by two leading researchers of the subjects, is not only a beautiful and accessible survey on del Pezzo surfaces and K3 surfaces, but also an excellent introduction to the general theory of Q-Fano varieties. 2006, 149p, ISBN:4-931469-34-5 | ||
| Vol.14 | Author: | Noboru Nakayama |
| Title: | Zariski-decomposition and Abundance | |
|
Dr. Noboru Nakayama, the author of this book, studies
the birational classification of algebraic varieties
and of compact complex manifolds.
This book is a collection of his works on the numerical
aspects of divisors of algebraic varieties. The notion of Zariski-decomposition introduced by Oscar Zariski is a powerful tool in the study of open surfaces. In the higher dimensional generalization, we encounter interesting phenomena on the numerical aspects of divisors. The author treats the higher dimensional Zariski-decomposition systematically. The abundance conjecture predicts that the numerical Kodaira dimension of a minimal variety coincides with the usual Kodaira dimension. The Kodaira dimension is an invariant of the canonical divisor of a variety. The numerical analogue used to be defined only for nef divisors, but it is now extended to arbitrary divisors in this book. Explained in details are many important results on the numerical Kodaira dimension related to the abundance, to the addition theorem for fiber spaces, and to the deformation invariance. 2004, 277p, ISBN:4-931469-31-0 | ||
| Vol.13 | Author: | Shigeaki Koike |
| Title: | A beginner's guide to the theory of viscosity solutions | |
|
The notion of viscosity solutions was first introduced by
M. G. Crandall and P.-L. Lions in 1981 to study first-order partial
differential equations of nondivergence form, typically,
Hamilton-Jacobi equations. Later, the study of viscosity solutions was
extended to second-order elliptic/parabolic equations. It has turned
out by many researchers that the viscosity solution theory is a
powerful tool to investigate fully nonlinear second-order (degenerate)
elliptic/parabolic equations arising in optimal control problems,
differential games, mean curvature flow, phase transitions,
mathematical finance, conservation laws, variational problems,
etc. This text is an introduction to the viscosity solution theory as
indicated by the title. After a brief history of weak solutions, it presents several uniqueness (comparison principle) and existence results, which are main issues. For further topics, it chooses generalized boundary value problems and regularity results. In Appendix, which is the hardest part, it provides proofs of several important propositions. Dr. Koike's current mathematical interests still lie in the viscosity solution theory and its applications. 2004, 132p, ISBN:4-931469-28-0, Not in stock |
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| Vol.12 | Author: |
Yves André (with appendices by F. Kato and N. Tsuzuki) |
| Title: |
Period mappings and differential equations.
Form C to C_p Tohoku-Hokkaido lectures in Arithmetic Geometry | |
|
The theorey of period mappings has played a central role in nineteen-century
mathematics as a fertile place of interaction between
algebraic and differential geometry, differential equations,
and group theory, from Gauss and Riemann to Klein and Poincaré.
This text is an introduction to the p-adic counterpart
of this theory, which is much more recent and still mysterious.
It should be of interest both to some complex geometers and
to some arithmetic geometers.
Starting with an introduction to p-adic analytic geometry (in the sense of Berkovich), it then presents the Rapoport-Zink theory of period mappings, emphasizing the relation with Picard-Fuchs differential equtions. a new theory of fundamental groups, orbifolds, and uniformizing equations (in the p-adic context) accounts for the group-theoretic aspects of these period mappings. The books ends with a theory of p-adictriangle groups. Dr. André's current mathematical interests lie in arithmetic geometry and in the theory of motives. 2003, 246p, ISBN4-931469-22-1, Not in stock | ||
| Vol.11 | Authors: | John R. Stembridge, Jean-Yves Thibon and Marc A. A. van Leeuwen |
| Title: | Interaction of combinatorics and representation theory | |
|
This volume consisting of two research papers
and one survey paper is a good guide to look into a new emerging field,
which stems from the interaction of combinatorics and representation
theory.
Dr. John Stembrige is famous for his study on combinatorics in Lie algebra representations, Coxeter/Weyl groups, and other topics. Also he is the author of the Maple package software ``SF'' (Schur functions), ``coxeter/weyl'', and ``posets''. Dr. Jean-Yves Thibon is one of the most active researchers in this field and is famous for many collaborated works with Alain Lascoux and Bernard Leclerc and other famous researchers. Dr. Marc van Leeuwen is famous in the field of manipulation of Young tableaux and its related topics. He is one of the authors of the software package ``LiE'' for Lie group computation. 2001, 145p, ISBN4-931469-14-0, Not in stock | ||
| Vol.10 | Author: | Yuri G. Prokhorov |
| Title: | Lectures on complements on log surfaces | |
|
Dr. Yuri Prokhorov, the author of this book, is an
expert in
birational geometry in the field of algebraic geometry.
This book is the first significant expository lecture for
``complements''; this notion was introduced by Vyacheslav Shokurov
quite recently and is important in understanding singularities
of a pair consisting of an algebraic variety and
a divisor on it.
There is currently much ongoing research on this subject,
a very active area in algebraic geometry.
This book helps the reader to understand the ``complement'' concept and provides the basic knowledge about the singularities of a pair. The author gives a simple proof of the boundedness of the complements for two dimensional pairs under some restrictive condition, where this boundedness has been conjectured by Shokurov for every dimension. This book contains information and encouragement necessary to attack the problem of the higher dimensional case. 2001, 130p, ISBN4-931469-12-4, Not in stock | ||
| Vol.9 | Authors: | Peter Orlik and Hiroaki Terao |
| Title: | Arrangements and hypergeometric integrals | |
|
An affine arrangement of hyperplanes is a finite collection of
one-codimensional affine linear spaces in Cn.
P. Orlik and H. Terao are leading specialists in the theory of
arrangements and the co-authors
of the well-known book ``Arrangements of Hyperplanes''.
In this monograph, they give an introductory survey which also
contains the recent progress
in the theory of hypergeometric functions.
The main argument is done from the arrangement-theoretic point of view.
This will be a nice text for a student to begin the study of
hypergeometric functions.
2001, 112p, ISBN4-931469-10-8, Not in stock | ||
| Vol.8 | Author: | Eric M. Opdam |
| Title: | Lecture notes on Dunkl operators for real and complex reflection groups | |
|
Eric M. Opdam studied a generalization of the system of
differential equations satisfies by the Harish-Chandra spherical functions,
and with Gerrit Heckman established the theory of Heckman-Opdam
hypergeometric functions by the use of a trigonometric extension of Dunkl
operators.
In this note he introduces this theory, and includes a recent result on the harmonic analysis of the hypergeometric functions and also an application of Dunkl operators to the study of reflection groups. 2000, 90p, ISBN4-931469-08-6, Not in stock | ||
| Vol.7 | Author: | Vladimir Georgiev |
| Title: | Semilinear hyperbolic equations | |
|
Most of the standard theorems of global in time existence for solutions of the
nonlinear evolution equations in mathematical physics depend heavily upon
estimates for the solution's total energy.
Typically, to prove the global existence of a smooth solution,
one argues that a certain amount of energy would necessarily be dissipated
in the development of a singularity,
which is limited by virtue of small data assumptions so far,
except for some semilinear evolution equations with good sign.
Under the small data assumption, the main observation is devoted to the investigation of the dissipative mechanism of linearized equations, which is described by the decay estimate of solutions mathematically. V. Georgiev is one of the most excellent mathematicians who created outstanding a priori estimates about hyperbolic equations in mathematical physics, which yield solutions of the corresponding nonlinear hyperbolic equations under small data assumption. The aim of this lecture note is to explain how to derive sharp a priori estimates which enable us to prove a global in time existence of solutions to semilinear wave equation and non-linear Klein-Gordon equation. The core of the lecture note is Section 8, which is devoted to Fourier transform on manifolds with constant negative curvature. Combining this with the interpolation method and psudodifferential operator approach enables us to obtain better Lp weighted a priori estimates. Key words: semilinear wave equation, Fourier transform on hyperboloid, Sobolev spaces on hyperboloid, Klein - Gordon equation 2000, 209p, ISBN4-931469-07-8, Not in stock | ||
| Vol.6 | Author: | Kong De-xing |
| Title: | Cauchy problem for quasilinear hyperbolic systems | |
|
This book is concerned with Cauchy problem for quasilinear hyperbolic
systems. By introducing the concepts weak linear degeneracy and
matching condition, we give a systematic presentation on the global
existence, the large time behaviour and the blow-up phenomenon,
particularly, the life span of C1
solutions to the Cauchy problem
with small and decaying initial data. Some successful applications of
our general theory are given to the quasilinear canonical system
related to the Monge-Amp\`ere equation, the system of nonlinear
three-wave interaction in plasma physics, the nonlinear wave equation
with higher order dissipation, the system of one-dimensional gas
dynamics with nonlinear dissipation, the system of motion of an
elastic string, the system of plane elastic waves for hyperelastic
materials and so on.
Key words and phrases: Quasilinear hyperbolic system, Cauchy problem, C1 solution, blow-up, life span. 2000, 213p, ISBN4-931469-06-X | ||
| Vol.5 | Authors: | Daryl Cooper, Craig D. Hodgson and Steven P. Kerckhoff |
| Title: | Three-dimensional orbifolds and cone-manifolds | |
|
This volume provides an excellent introduction of
the statement and main ideas in the proof
of the orbifold theorem announced by Thurston in late 1981.
It is based on the authors' lecture series
entitled
``Geometric Structures on 3-Dimensional Orbifolds"
which was featured in the third MSJ Regional Workshop on
``Cone-Manifolds and Hyperbolic Geometry"
held on July 1-10, 1998, at
Tokyo Institute of Technology.
The orbifold theorem shows the existence of geometric
structures on many 3-orbifolds and
on 3-manifolds with symmetry.
The authors develop the basic
properties of orbifolds and
cone-manifolds,
extends many ideas from the
differential geometry to
the setting of cone-manifolds
and outlines a proof of the orbifold theorem.
2000, 170p, ISBN4-931469-05-1, Not in stock | ||
| Vol.4 | Authors: | Atsushi Matsuo and Kiyokazu Nagatomo |
| Title: | Axioms for a vertex algebra and the locality of quantum fields | |
|
Dr. A. Matsuo has been working on various mathematical
structures related to two-dimensional conformal field theory.
He is famous for his study on the Knizhnik-Zamolodchkov
equation and its analogues. He is recently interested in
searching for examples of vertex algebras having interesting
symmetries.
Dr. K. Nagatomo is working on the theory of vertex oeprator algebras and related topics. His interests include applications of the representation theory of infinite dimensional algebras to completely integrable systems. He dedicates this paper to Dr. Matsuo's daughter who was born a few days ago. 1999, 110p, ISBN4-931469-04-3 | ||
| Vol.3 | Author: | Tomotada Ohtsuki |
| Title: | Combinatorial quantum method in 3-dimensional topology | |
|
This book is based on
a series of lectures by the author
in the workshop
"Combinatorial Quantum Method in
3-dimensional Topology"
held in
Oiwake Seminar House of Waseda University
in the end of September, 1996.
After the discovery of the Jones polynomial at the middle of 1980's, many new invariants of knots and 3-manifolds, what we call quantum invariants, have been found. At the present we have two key words to understand quantum invariants of knots; "the Kontsevich invariant" and "Vassiliev invariants". Correspondingly we have also two notions for 3-manifold invariants; "The LMO invariant" and "finite type invariants". The aim of this book is to explain about construction and basic properties of these invariants and how to understand quantum invariants via these invariants. 1999, 83p, ISBN4-931469-03-5, Not in stock | ||
| Vol.2 | Authors: | Masako Takahashi, Mitsuhiro Okada and Mariangiola Dezani-Ciancaglini (Eds.) |
| Title: | Theories of types and proofs | |
|
This is an excellent collection of refereed articles
on theories of types and proofs. The articles are written
by noted experts in the area.
In addition to the value of the individual articles,
the collection is notable for covering a range of related topics.
The collection begins with useful primer on the subject that
will make the subsequent articles more accessible to potential
readers. Following the primer,
there are good articles on traditional topics in type assignment systems.
These are followed by explanations of applications to program analysis
and a series of articles on application to logic. The collection
includes articles on intuitionistic logic,
a standard use of type-theoretic notions, and concludes with an article
on linear logic.
1998, 295p, ISBN4-931469-02-7 | ||
| Vol.1 | Authors: | Ivan Cherednik, Peter J. Forrester and Denis Uglov |
| Title: | Quantum many-body problems and representation theory | |
|
Dr. I. Cherednik is famous for introducing the double affine Hecke
algebras, which is the main topics in his article
``Lectures on affine Knizhnik-Zamolodchikov equations, . . .''.
This focuses on the equivalence of the affine Knizhnik-Zamolodchikov
equations and the quantum many-body problems. It also serves as
an introduction to the new theory of the spherical and
the hypergeometric functions based on the affine and the double affine
Hecke algebras.
Dr. P. J. Forrester is an expert in random matrix theory and Coulomb systems. Dr. Forrester has also been a pioneer in the application of Jack symmetric functions to statistical physics. The article ``Random Matrices, Log-Gases and the Calogero-Sutherland Model'' deals precisely with these three areas. Dr. D. Uglov is actively working in the quantum many-body problems and the related representation theory. The article ``Symmetric functions and the Yangian decomposition . . .'' is an exposition of his recent works on these topics. 1998, 241p, ISBN4-931469-01-9, Not in stock | ||
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