A comprehensive graduate-level textbook that takes a fresh approach to complex analysis
Hardcover
ISBN: 9780691207582
Oct 12, 2021
Pages: 448
Size: 8 x 10 in.
Illus:77 color + 63 b/w illus. 2 tables
A Course in Complex Analysis explores a central branch of mathematical analysis, with broad applications in mathematics and other fields such as physics and engineering. Ideally designed for a year-long graduate course on complex analysis and based on nearly twenty years of classroom lectures, this modern and comprehensive textbook is equally suited for independent study or as a reference for more experienced scholars.
Saeed Zakeri guides the reader through a journey that highlights the topological and geometric themes of complex analysis and provides a solid foundation for more advanced studies, particularly in Riemann surfaces, conformal geometry, and dynamics. He presents all the main topics of classical theory in great depth and blends them seamlessly with many elegant developments that are not commonly found in textbooks at this level. They include the dynamics of Mobius transformations, Schlicht functions and distortion theorems, boundary behavior of conformal and harmonic maps, analytic arcs and the general reflection principle, Hausdorff dimension and holomorphic removability, a multifaceted approach to the theorems of Picard and Montel, Zalcmanfs rescaling theorem, conformal metrics and Ahlforsfs generalization of the Schwarz lemma, holomorphic branched coverings, geometry of the modular group, and the uniformization theorem for spherical domains.
Written with exceptional clarity and insightful style, A Course in Complex Analysis is accessible to beginning graduate students and advanced undergraduates with some background knowledge of analysis and topology. Zakeri includes more than 350 problems, with problem sets at the end of each chapter, along with numerous carefully selected examples. This well-organized and richly illustrated book is peppered throughout with marginal notes of historical and expository value.
Presenting a wealth of material in a single volume, A Course in Complex Analysis will be a valuable resource for students and working mathematicians.
A groundbreaking contribution to number theory that unifies classical and modern results
Series: : Annals of Mathematics Studies 212
Hardcover
ISBN: 9780691216478
Paperback
ISBN: 9780691216461
Nov 9, 2021
Pages:280
Size: 6.13 x 9.25 in.
This book develops a new theory of p-adic modular forms on modular curves, extending Katzfs classical theory to the supersingular locus. The main novelty is to move to infinite level and extend coefficients to period sheaves coming from relative p-adic Hodge theory. This makes it possible to trivialize the Hodge bundle on the infinite-level modular curve by a gcanonical differentialh that restricts to the Katz canonical differential on the ordinary Igusa tower. Daniel Kriz defines generalized p-adic modular forms as sections of relative period sheaves transforming under the Galois group of the modular curve by weight characters. He introduces the fundamental de Rham period, measuring the position of the Hodge filtration in relative de Rham cohomology. This period can be viewed as a counterpart to Scholzefs Hodge-Tate period, and the two periods satisfy a Legendre-type relation. Using these periods, Kriz constructs splittings of the Hodge filtration on the infinite-level modular curve, defining p-adic Maass-Shimura operators that act on generalized p-adic modular forms as weight-raising operators. Through analysis of the p-adic properties of these Maass-Shimura operators, he constructs new p-adic L-functions interpolating central critical Rankin-Selberg L-values, giving analogues of the p-adic L-functions of Katz, Bertolini-Darmon-Prasanna, and Liu-Zhang-Zhang for imaginary quadratic fields in which p is inert or ramified. These p-adic L-functions yield new p-adic Waldspurger formulas at special values.
The text provides a self-contained and efficient one-semester introduction to
the main concepts and results in convex geometry.
The selected topics highlight the interactions between geometry and analysis,
treating several topics for the first time in an introductory textbook.
Suggestions for further reading and a large number of solved exercises
complement the main text
This book providesa self-contained introduction toconvex geometry in Euclidean space.After
covering the basic concepts and results, it developsBrunn?Minkowskitheory, with an exposition
of mixed volumes, the Brunn?Minkowski inequality, and some of its consequences,includingthe
isoperimetric inequality.Further centraltopics are then treated, such as surface area measures,
projection functions, zonoids, and geometric valuations.Finally, an introduction tointegralgeometric
formulas in Euclidean space is provided.The numerous exercises and the
supplementary material at the end of each sectionform an essential partof the book. Convexity
is an elementary and naturalconcept.It plays a key role in many mathematical fields, including
functional analysis,optimization,probability theory,and stochastic geometry. Paving the way to
the more advanced and specialized literature, thematerialwill beaccessible to students in the
third year and can be coveredin one semester.
1st ed. 2020, XVIII, 287 p.
11 illus., 9 illus. in color.
Hardcover : ISBN 978-3-030-50179-2
Product category : Graduate/advanced undergraduate textbook
Series : Graduate Texts in Mathematics
Softcover : ISBN 978-3-030-50182-2
Mathematics : Convex and Discrete Geometry
*
Provides an introduction to some key subjects in algebra and topology
Consists of comprehensive texts on the preliminaries for several advanced
theories in algebra and topology
Helps young researchers to quickly get into the subject
This book provides an introduction to some key subjects in algebra and topology. It consists of
comprehensive texts of some hours courses on the preliminaries for several advanced theories
in (categorical) algebra and topology. Often, this kind of presentations is not so easy to find in
the literature, where one begins articles by assuming a lot of knowledge in the field. This
volume can both help young researchers to quickly get into the subject by offering a kind of
ároadmapâ and also help master students to be aware of the basics of other research
directions in these fields before deciding to specialize in one of them. Furthermore, it can be
used by established researchers who need a particular result for their own research and do
not want to go through several research papers in order to understand a single proof.Although
the chapters can be read as áself-containedâ chapters, the authors have tried to coordinatethe
texts in order to make them complementary. The seven chapters of this volume correspond to
the seven courses taught in two Summer Schools that took place in Louvain-la-Neuve in the
frame of the project Fonds dfAppui a lfInternationalisation of the Universite catholique de
Louvain to strengthen the collaborations with the universities of Coimbra, Padova and Poitiers,
within the Coimbra Group.
Due 2021-11-01
1st ed. 2021, X, 233 p. 3 illus.
Hardcover
ISBN 978-3-030-84318-2
Product category : Graduate/advanced undergraduate textbook
Series : Coimbra Mathematical Texts
Mathematics : Algebra
The first systematic introduction to non-Euclidean Laguerre geometry in the
literature
Demonstrates all features of Laguerre geometry in terms of one recent
application: checkerboard incircular nets
Beautifully illustrated by many render images
This textbook is a comprehensive and yet accessible introduction to non-Euclidean
Laguerregeometry, for which there exists no previous systematic presentation in the literature.
Moreover, we present new results by demonstrating all essential features of Laguerre geometry
on theexample of checkerboard incircular nets. Classical (Euclidean) Laguerre geometry studies
oriented hyperplanes, oriented hyperspheres, and their oriented contact in Euclidean space. We
describe how this can be generalized to arbitrary Cayley-Klein spaces, in particular hyperbolic
and elliptic space, and study the corresponding groups of Laguerre transformations. We give an
introduction to Lie geometry and describe how these Laguerre geometries can be obtained as
subgeometries. As an application of two-dimensional Lie and Laguerre geometry we study the
properties of checkerboard incircular nets.
Due 2021-10-29
1st ed. 2021, X, 137 p. 58 illus., 53 illus. in color.
Softcover : ISBN 978-3-030-81846-3
Product category : Brief
Series : SpringerBriefs in Mathematics
Mathematics : Geometry
Includes an overview over Ron Doney's scientific achievements
Presents research articles from renowned researchers
Covers research fields influenced by Ron Doney
This collection honours Ron Doneyfs work and includes invited articles by his collaborators and
friends. After an introduction reviewing Ron Doneyfs mathematical achievements and how they
have influenced the field, the contributed papers cover both discrete-time processes, including
random walks and variants thereof, and continuous-time processes, including Levy processes
and diffusions. A good number of the articles are focused on classical fluctuation theory and
its ramifications, the area for which Ron Doney is best known.
Due 2021-11-07
1st ed. 2021, X, 290 p. 7 illus. in color.
Hardcover : ISBN 978-3-030-83308-4
Product category : Contributed volume
Series : Progress in Probability
Mathematics : Probability Theory and Stochastic Processes
Covers the latest achievements in nonsmooth analysis, with applications in
mechanics, engineering and game theory
Presents a set of arguments for investigating (smooth or nonsmooth) elliptic PDEs
Provides a detailed background in the appendices, making the book selfcontained
This book provides a modern and comprehensive presentation of a wide variety of problems
arising in nonlinear analysis, game theory, engineering, mathematical physics and contact
mechanics. It includes recent achievements and puts them into the context of the existing
literature. The volume is organized in four parts. Part I contains fundamental mathematical
results concerning convex and locally Lipschits functions. Together with the Appendices, this
foundational part establishes the self-contained character of the text. As the title suggests, in
the following sections, both variational and topological methods are developed based on
critical and fixed point results for nonsmooth functions. The authors employ these methods to
handle the exemplary problems from game theory and engineering that are investigated in
Part II, respectively Part III. Part IV is devoted to applications in contact mechanics. The book
will be of interest to PhD students and researchers in applied mathematics as well as
specialists working in nonsmooth analysis and engineering.
Due 2021-10-20
1st ed. 2021, XVI, 446 p. 3 illus. in color.
Softcover : ISBN 978-3-030-81670-4
Product category : Monograph
Series : Frontiers in Mathematics
Mathematics : Analysis