Softcover ISBN: 978-1-4704-8379-1
Product Code: STML/109
Expected availability date: January 10, 2026
Student Mathematical Library
Volume: 109; 2025; Estimated: 241 pp
MSC: Primary 37; 51; 52
This richly illustrated text guides readers to discover the beautiful structure of mathematical billiards. Centered around expertly designed problem sets, the book incrementally builds up ideas through threads of related problems, fostering curiosity, exploration, and conversation. Working through the problems, the reader builds an understanding of foundational results, useful techniques, and key examples, all the way up to current research, while hands-on construction activities offer an opportunity to explore phenomena in three dimensions.
Beginning with the square billiard table, the opening chapters explore periodic billiard paths in depth, including connections to continued fractions and symbolic dynamics. From this foundation, the book goes on to explore billiards in triangles and other polygons, flows on translation surfaces, interval exchange transformations, outer billiards and tiling billiards, billiards on the ellipse, and many other topics. Throughout, we meet contemporary mathematicians involved in the topics covered, showcasing the research achievements of the vibrant billiards community.
Billiards, Surfaces, and Geometry offers a ground level, problem-centered entry point to this exciting field. Basic knowledge of geometry and matrix transformations is assumed, though the main prerequisite is a spirit of curiosity and exploration.
Graduate students interested in discovering the geometric structure behind mathematical billiards.
Introduction to billiards in many forms
Trajectories, automorphisms, and continued fractions
Periodicity everywhere
Cylinders and automorhpisms
Further topics and tools
A short primer on matrix actions in the plane
How to teach a problem-centered course
Image credits
Hints for selected problems
Bibliography
Glossary of key terms
Index of terms
Index of people
This volume is dedicated to Nina Nikolaevna Uraltseva on the occasion of her 90th birthday. It collects contributions by her numerous colleagues and friends sharing with her research interests in linear and quasilinear elliptic and parabolic equations, degenerate and geometric equations, variational inequalities, and free boundary problems.
In brief, the topics covered include regularity for transmission systems, bifurcation of solitary waves, parabolic equations with Morrey lower-order coefficients, mesoscopic modeling of optimal transportation networks, Sobolev regularity in nonlinear elliptic problems, planar loops with prescribed curvature, interface behavior for the solutions of free boundary problems, a multi-phase Stefan problem, homogenization of nonlocal convolution-type operators, an obstacle-type problem for the p-Laplacian with the fractional gradient, scalar variational problems with maximal singular sets, bifurcations in the Lotka–Volterra competition model, and the Dirichlet-area minimisation problem. In addition, the volume contains a description of Uraltseva’s main contributions to mathematics and the mathematical community
Format: Hardback, 239 pages, height x width: 235x155 mm, 15 Illustrations, color;
30 Illustrations, black and white; X, 239 p. 45 illus., 15 illus. in color., 1 Hardback
Series: KIAS Springer Series in Mathematics 5
Pub. Date: 03-Oct-2025
ISBN-13: 9789819503841
This open access book is a tribute to the profound contributions of Professor Bumsig Kim in the field of mathematics, particularly in the realm of mirror symmetry. Mirror symmetry is a fascinating duality between complex/algebraic geometry and symplectic geometry, manifesting in various ways. One of the foundational examples of this duality is the comparison of period integrals on a complex manifold with curve counts (enumerative invariants) on its mirror. This vision was ultimately realized through the Quasimap Wall-Crossing Formula, developed by Bumsig Kim and his collaborators.
The book delves into the methods for counting curves, including Gromov–Witten theory and Fan–Jarvis–Ruan–Witten theory. In his final works, Kim and various groups of collaborators achieved methods for counting curves on gauged linear sigma models, effectively unifying Gromov–Witten and Fan–Jarvis–Ruan–Witten theory. This monumental effort involved constructing categorical frameworks and developing a dictionary between categorical and classical homological constructions.
As a conference proceedings volume, this book is a collaborative effort by Professor Kim’s network of colleagues. It explores the intricate connections between categorical and enumerative aspects of mirror symmetry, showcasing the depth and breadth of Kim's work. Through detailed discussions and presentations, the book highlights the innovative approaches and groundbreaking results that have shaped the field.
Readers will find a comprehensive overview of the latest advancements in mirror symmetry, enriched by the collaborative spirit and intellectual rigor that characterized Professor Kim's career. This volume not only honors his legacy but also serves as a valuable resource for researchers and students seeking to understand and build upon his pioneering work. Whether you are new to the field or an experienced mathematician, this book offers a wealth of knowledge and insights into the complex and beautiful world of mirror symmetry.
Bibliog. data: 2025. xiv, 353 S. XIV, 353 p. 130 illus., 18 illus. in color. 235 mm
Format: Kartoniert
Series: UNITEXT 172
ISBN-13: 9783031929120
Hardback
This book shows hundreds of guided problems, with very detailed explanation on how to go about finding the right argument. This is the second of a 3-book project, the first book being already published (Calculus Problems, UNITEXT 101). The style, therefore, follows closely that of the aforementioned volume, with improvements in the graphic packaging, due to updating of the used software and the inclusion of further graphical packages. Each chapter contains a summary of the relevant definitions and theorems, a section with worked problems and a section on suggested exercises with solutions. This second book includes an elementary but thorough introduction to basic topology of Euclidean spaces and then focusses on of functions of several variables and on multiple integrals, sequences and series of functions.It is addressed to UG students based both in EU and USA.
Structures and Functions on Euclidean Space.- Limits and Continuity.- Differentiation.- Minima and Maxima, Implicit Functions.- Multiple Integrals.- Sequences and Series of Functions.
Marco Baronti was born and grew up in Genova (Italy) where he got his Laurea in Mathematics in 1979. He won a scholarship from the C.N.R. in Genoa and subsequently a research grant from I.N.D.A.M. at the University of Bologna. In 1984 he became a researcher at the University of Parma and then associate professor in 1987 at the University of Ancona. In 1991 he returned to Genova, where he presently holds a position as associate professor in Mathematical Analysis.Enrico Calcagno was born and grew up in Genova (Italy) where he got his Laurea in Mathematics. He started his tenured position at the University of Genova in 1981. His scientific interests are mainly in Differential Geometry and Algebraic Topology. He has been involved for about forty years in a wide teaching activity for mathematicians, physicists, chemists, biologists, computer scientists, geologists and engineers.Filippo De Mari was born and grew up in Genova (Italy) where he got his Laurea in Mathe
matics in 1983. He obtained his Ph.D. in 1987 from Washington University in St. Louis (USA) and then held two post-doctoral positions in Bremen (Germany) 1988-89 and Torino (Italy) 1990-92. In 1992 he returned to Genova, where he presently holds a position as full professor in Mathematical Analysis.Robertus van der Putten was born and grew up in Sanremo (Italy). He got his Laurea in Mathematics in 1984 at the University of Genova. He obtained his Ph.D. in 1989 from the University of Milan. Since 1990, he is a researcher in Mathematical Analysis at the University of Genoa.His scientific interests are mainly in the Calculus of Variations. His main scientific interests may be grouped into following main areas. The first concerns the properties of energy functional integrals in the setting of nonlinear elasticity and the existence of the minimum in Sobolev spaces.
Format: Hardback, 146 pages, height x width: 235x155 mm, 73 Illustrations, color; 1 Illustrations,
black and white; X, 146 p. 74 illus., 73 illus. in color., 1 Hardback
Series: ICIAM2023 Springer Series 7
Pub. Date: 16-Oct-2025
ISBN-13: 9789819690862
This book presents a curated collection of recent research contributions in the field of nonlinear partial differential equations (PDEs), with an emphasis on hyperbolic problems. These equations are essential for modeling complex physical phenomenasuch as wave propagation, fluid dynamics, blood flow, and sediment transport. In many real-world applications, the governing equations are not purely hyperbolic but involve intricate interactions with elliptic or parabolic components.
As the field advances through theoretical insights and practical needs, this volume captures innovative developments shaping current research. The contributions included here were originally presented at the 10th International Congress on Industrial and Applied Mathematics (ICIAM), held in Tokyo in 2023. Selected from minisymposia on hyperbolic PDEs and related topics, each organized by leading experts in the field.
The chapters in this book reflect a rich diversity of perspectives and approaches, ranging from rigorous mathematical analysis to computational techniques and real-world applications. By bringing together these works, the volume offers a comprehensive snapshot of the state of the art in hyperbolic PDE research, highlighting both foundational insights and emerging trends.
Edited by the organizers of the relevant ICIAM 2023 minisymposia, this book serves as a valuable resource for researchers, practitioners, and graduate students interested in the theoretical and applied aspects of nonlinear PDEs. Whether you are exploring the mathematical underpinnings of wave phenomena or developing models for complex systems in science and engineering, this volume provides both inspiration and practical tools to advance your work.
Chapter 1 A comparison of the Coco-Russo scheme and -FEM for elliptic equations in arbitrary domains.
Chapter 2 A semi-implicit method for a degenerating convection-diffusion-reaction problem modeling secondary settling tanks.
Chapter 3 Multidimensional approximate Riemann solvers for hyperbolic nonconservative systems: a review.
Chapter 4 Challenges in Stochastic Galerkin Methods for Nonlinear Hyperbolic Systems with Uncertainty.
Chapter 5 On the role of momentum correction factor and general tube law in one-dimensional blood flow models for networks of vessels.-
Chapter 6 Numerical modelling of the hemodynamic changes in the inferior vena cava in response to the Valsalva maneuver.
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Format: Hardback, 360 pages, height x width: 235x155 mm, Approx. 360 p., 1 Hardback
Series: Springer Asia Pacific Mathematics Series 3
Pub. Date: 25-Sep-2025
ISBN-13: 9789819503544
Goodreads reviews
The core of this book is variational methods and their applications in geometry, physics, mechanics engineering control and economics. The author set out to solve the classical and famous problems including Isoperimetric Problem, Brachistochrone Curve Problem, N-Body Problems, Geodesic Curve Problem, Minimal Surface Problem, Dirichlet Principle, Minimax Problems, Rabinowitz Minimal Period Conjecture, etc. The book contains many interesting historic backgrounds and important examples, explains profound theories in simple language, which can help readers to follow in order and advance step by step. The proofs for very difficult theorems are also clearly expressed, and all chapters and appendixes are very well-written. The book has 8 organized appendixes that are important and appropriate supplements to the main texts. Appendices 1 to 7 are related with some famous classical theorems while Appendix 8 is related with the famous Rabinowitz's minimum period conjecture.
The level of this book is between the textbook for graduate students and monograph. The prerequisites on Calculus, Classical Mechanics, Ordinary Differential Equations and Real and Functional Analysis are required. It is very useful for graduate students in mathematics, physics, mechanics and related engineering majors who want to improve their knowledge in Nonlinear Sciences.
Bibliog. data: January 2026. 590 S. Approx. 590 p. 235 mm
Series: Graduate Texts in Mathematics 308
ISBN-13: 9783032038982
This graduate textbook introduces the unitary representation theory of groups, emphasizing applications in fields like dynamical systems.It begins with the general theory and motivation, then explores key classes of groups. Abelian and compact groups are treated through Pontryagin duality and the Peter Weyl theorem. Metabelian groups illustrate links to ergodic theory and lead to the Mackey machine. Weak containment and the Fell topology are introduced through examples. The final chapters apply the theory to special linear groups in dimensions two and three, covering smooth vectors, spectral gaps, and decay of matrix coefficients. The two-dimensional case is examined in depth, including the Kunze Stein phenomenon, spectral decomposition on the hyperbolic plane, and the Weil representation. The book concludes with a full description of the unitary dual of SL(2,R) and its Fell topology, applying the theory to prove effective equidistribution of horocycle orbits.W
ith its focus on key examples and concrete explanations, this textbook is aimed at graduate students taking first steps in unitary representation theory. It builds the theory from the ground up, requiring only some familiarity with functional analysis beyond standard undergraduate mathematics.
1 Unitary Representations.- 2 Abelian Groups.- 3 Compact Groups.- 4 Lie Algebras and Unitary Representations of SU2(R).- 5 Normal Abelian Subgroups and Unitary Duals.- 6 Weak Containment and the Fell Topology.- 7 Smooth Vectors and Decay for SL3(R).- 8 Discrete Series Representations and Temperedness.- 9 Unitary Representations of SL2(R).- Appendix A: Linear Algebra.- Appendix B: Analysis.- Appendix C: Topological Groups.
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October 2025
Pages: 200
ISBN: 978-981-12-9516-4 (hardcover)
The aim of this book is to provide a pedagodical yet comprehensive review of various aspects of four-dimensional Chern-Simons theory, a quantum field theory that has emerged as an organizing principle for various integrable systems, such as integrable spin chains, integrable lattice models, and two-dimensional integrable quantum field theories. Among topics covered are the derivation of the Yang-Baxter equation and its solutions, the Yangian algebra, realizations of two-dimensional integrable field theories and their Lax operators, string-theoretic embeddings of four-dimensional Chern-Simons theory, holographic duals of the theory, as well as dualities of integrable quantum field theories.
Integrable Lattice Models
Integrable Field Theories
4D Chern-Simons Theory from Supersymmetric Gauge Theory and String Theory
4D Chern-Simons Theory with Boundary and Holography
Towards Quantization of Integrable Field Theories
Readership: The target readership primarily consists of researchers working on high energy physics , mathematical physics, and mathematicians studying quantum groups. This includes advanced postgraduate students. This book could be useful for advanced courses on quantum field theory and integrable systems.