ISBN: 978-3-031-32114-6
Subject: Mathematics and Statistics
Planned Publication Date: 2023年7月20日
Series Title: Oberwolfach Seminars
Resolution of singularities is notorious as a difficult topic within algebraic geometry. Recent work, aiming at resolution of families and semistable reduction, infused the subject with logarithmic geometry and algebraic stacks, two techniques essential for the current theory of moduli spaces. As a byproduct a short, a simple and efficient functorial resolution procedure in characteristic 0 using just algebraic stacks was produced.
The goals of the book, the result of an Oberwolfach Seminar, are to introduce readers to explicit techniques of resolution of singularities with access to computer implementations, introduce readers to the theories of algebraic stacks and logarithmic structures, and to resolution in families and semistable reduction methods.
Dan Abramovich studied mathematics at Tel Aviv University and at Harvard, where he received his PhD in 1991. After a postdoctoral fellowship at MIT, he was on faculty at Boston University, where he was Sloan Research Fellow, before moving to Brown University where he is L. Herbert Ballou University Professor. He is Fellow of the American Mathematical Society and the American Association for the Advancement of Science. He works in birational Geometry, Moduli Spaces, and Arithmetic Geometry. His 2018 ICM talk at Rio de Janeiro focused on material described in the present book.
Anne Fruhbis-Kruger works in computational algebraic geometry and singularity theory. She received her PhD from Kaiserslautern University in 2000. After a visiting professorship at FU Berlin and more than a decade as apl. Professor at Leibniz Universitat Hannover, she moved to her current position at Universitat Oldenburg in 2019. She has served as the spokesperson of the 'Fachgruppe Computeralgebra' for two periods and is actively involved in the development of the computer algebra systems Singular and OSCAR.
Michael Temkin is the Maurice and Clara Weil Chair in Mathematics at the Hebrew University of Jerusalem. His main research interests lie within non-archimedean geometry, birational geometry and the interplay between them. In particular, he is interested in resolution of singularities and semistable reduction problems. He graduated from the Weizmann Institute of Science in 2006, and after a postdoc at the University of Pennsylvania and a one-year membership at the IAS joined the Hebrew University of Jerusalem in 2010. Since 2020 he is serving as the editor in chief of the Israel Journal of Mathematics.
Jaros?aw W?odarczyk works in birational geometry and resolution of singularities. He graduated from Warsaw University in 1993. After a visiting position in Ruhr University Bochum and a scholarship at Grenoble University, he joined Warsaw University where he worked till 2000. After that he moved to Purdue University, where he is now a professor at the Department of Mathematics. Jaros?aw W?odarczyk was an invited speaker in ICM Madrid 2006, where he presented his work on the weak Factorization Theorem, playing an important role in Algebraic Geometry. He is also a recipient of numerous awards for his research contributions to birational geometry.
ISBN: 978-3-031-31560-2
Subject: Mathematics and Statistics
Planned Publication Date: 2023年7月31日
Series Title: Developments in Mathematics
This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations.
The ultimate goal in Volume V is to prove well-posedness and Fredholm solvability results concerning boundary value problems for elliptic second-order homogeneous constant (complex) coefficient systems, and domains of a rather general geometric nature. The formulation of the boundary value problems treated here is optimal from a multitude of points of view, having to do with geometry, functional analysis (through the consideration of a large variety of scales of function spaces), topology, and partial differential equations.
ISBN: 978-3-031-32141-2
Subject: Mathematics and Statistics
Planned Publication Date: 2023年7月24日
Series Title: UNITEXT, La Matematica per il 3+2
This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; con- nectedness and compactness; Alexandrov compactification; quotient topol- ogies; countability and separation axioms; prebasis and Alexander's theorem; the Tychonoff theorem and paracompactness; complete metric spaces and function spaces; Baire spaces; homotopy of maps; the fundamental group; the van Kampen theorem; covering spaces; Brouwer and Borsuk's theorems; free groups and free product of groups and basic category theory. While it is very concrete at the beginning, abstract concepts are gradually introduced.
This second edition contains a new chapter with a topological introduction to sheaf cohomology and applications. It also corrects some inaccuracies and some additional exercises are proposed.
The textbook is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.
Marco Manetti (born 1966) is full professor in geometry at Sapienza University of Rome (Italy). His research activity concerns algebraic geometry, deformation theory and higher algebraic structures. He is author of the books "Topologia'' (Italian, 2008,2014), "Topology'' (2015) and "Lie methods in deformation theory'' (2022), all of them published with Springer.
ISBN: 978-3-031-33045-2
Subject: Mathematics and Statistics
Planned Publication Date: 2023年8月11日
Series Title: Applied Mathematical Sciences
This book introduces the reader to the study of Hamiltonian systems, focusing on the stability of autonomous and periodic systems and expanding to topics that are usually not covered by the canonical literature in the field. It emerged from lectures and seminars given at the Federal University of Pernambuco, Brazil, known as one of the leading research centers in the theory of Hamiltonian dynamics.
This book starts with a brief review of some results of linear algebra and advanced calculus, followed by the basic theory of Hamiltonian systems. The study of normal forms of Hamiltonian systems is covered by Ch.3, while Chapters 4 and 5 treat the normalization of Hamiltonian matrices. Stability in non-linear and linear systems are topics in Chapters 6 and 7. This work finishes with a study of parametric resonance in Ch. 8. All the background needed is presented, from the Hamiltonian formulation of the laws of motion to the application of the Krein-Gelfand-Lidskii theory of strongly stable systems.
With a clear, self-contained exposition, this work is a valuable help to advanced undergraduate and graduate students, and to mathematicians and physicists doing research on this topic.
Hildeberto Cabral is an Emeritus Professor at the Federal University of Pernambuco, Brazil. He did his PhD at the University of California, Berkeley (1972), after getting a Master's degree from the Institute of Pure and Applied Mathematics?IMPA, Brazil. He does research on dynamical systems, focusing on Hamiltonian systems, celestial mechanics, stability of equilibria, and periodic solutions.
Lucia Brandao Dias is an Associate Professor at the Federal University of Rondonia, Brazil. She holds a PhD in Mathematics (2007) from the Federal University of Pernambuco, Brazil, with post-doc studies at the same university. Her research interests lie in Hamiltonian systems, differential equations, and n-body problems.
ISBN: 978-981-99-2069-3
Subject: Mathematics and Statistics
Planned Publication Date: 2023年9月2日
Fractional calculus and its applications are fascinating research areas in many engineering disciplines. This book is a comprehensive collection of research from the author's group, which is one of the most active in the fractional calculus community worldwide and is the birthplace of one of the four MATLAB toolboxes in fractional calculus, the FOTF Toolbox. The book presents high-precision solution algorithms for a variety of fractional-order differential equations, including nonlinear, delay, and boundary value equations. Currently, there are no other universal solvers available for the latter two types of equations.
Through this book, readers can systematically study the mathematics and solution methods in the field of fractional calculus and apply these concepts to different engineering fields, particularly control systems engineering.
This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.
Xue Dingyu, received his doctorate from Sussex University in 1992, and took his post at Northeastern University in China in 1993, where he was promoted to full professorship in 1997. He started his teaching work on MATLAB since 1990, where he designed a Lab Demonstration GUI for Classroom in Sussex University, while he we doing his D Phil research. In 1996, he published his first MATLAB book in Chinese, entitled “Computer aided Control System Design with MATLAB Applications” in Tsinghua University Press in China, which was regarded the first in China, and one of the first few earliest ones in the world. In 30+ years of time, he has published 12 books in English plus numerous books in Chinese. The recent ones are the six-volume works on scientific computing and simulation, published in De Gruyter, Berlin, in 2020-2022.
He received many teaching honors and awards in China, for National-level Elite Courses, Textbooks, and National First-class Undergraduate courses, and national-level Educational Awards. He is the co-founder and vice-chair of the Fractional-order Systems and Control Committee, China Automation Association. He received two China Natural Science Foundation grants on fractional systems. Co-author (4th) of the 2010 Springer monograph on fractional calculus, Author of the 2017 De Gruyter monograph on Fractional calculus and fractional-order control. He is the author of the FOTF MATLAB Toolbox, one of the four most widely used MATLAB tools in the fractional calculus community worldwide.
Bai Lu, was a PhD candidate under Xue Dingyu’s supervision. He received his doctorate from Northeastern University in 2018, with many contributions in high-precision algorithms. He is now a lecturer in Shenyang University. He is also the co-author of the Chinese version of the proposed monograph.