Building Bridges Between Algebra and Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Building Bridges Between Algebra and Topology write by Wojciech Chachólski. This book was released on 2018-03-31. Building Bridges Between Algebra and Topology available in PDF, EPUB and Kindle. This volume presents an elaborated version of lecture notes for two advanced courses: (Re)Emerging methods in Commutative Algebra and Representation Theory and Building Bridges Between Algebra and Topology, held at the CRM in the spring of 2015. Homological algebra is a rich and ubiquitous area; it is both an active field of research and a widespread toolbox for many mathematicians. Together, these notes introduce recent applications and interactions of homological methods in commutative algebra, representation theory and topology, narrowing the gap between specialists from different areas wishing to acquaint themselves with a rapidly growing field. The covered topics range from a fresh introduction to the growing area of support theory for triangulated categories to the striking consequences of the formulation in the homotopy theory of classical concepts in commutative algebra. Moreover, they also include a higher categories view of Hall algebras and an introduction to the use of idempotent functors in algebra and topology.
Equivariant Topology and Derived Algebra
Equivariant Topology and Derived Algebra - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Equivariant Topology and Derived Algebra write by Scott Balchin. This book was released on 2021-11-18. Equivariant Topology and Derived Algebra available in PDF, EPUB and Kindle. A collection of research papers, both new and expository, based on the interests of Professor J. P. C. Greenlees.
Lecture Notes in Algebraic Topology
Lecture Notes in Algebraic Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lecture Notes in Algebraic Topology write by James F. Davis. This book was released on 2023-05-22. Lecture Notes in Algebraic Topology available in PDF, EPUB and Kindle. The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the “big picture”, teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.
Building Bridges between Soft and Statistical Methodologies for Data Science
Building Bridges between Soft and Statistical Methodologies for Data Science - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Building Bridges between Soft and Statistical Methodologies for Data Science write by Luis A. García-Escudero. This book was released on 2022-08-24. Building Bridges between Soft and Statistical Methodologies for Data Science available in PDF, EPUB and Kindle. Nowadays, data analysis is becoming an appealing topic due to the emergence of new data types, dimensions, and sources. This motivates the development of probabilistic/statistical approaches and tools to cope with these data. Different communities of experts, namely statisticians, mathematicians, computer scientists, engineers, econometricians, and psychologists are more and more interested in facing this challenge. As a consequence, there is a clear need to build bridges between all these communities for Data Science. This book contains more than fifty selected recent contributions aiming to establish the above referred bridges. These contributions address very different and relevant aspects such as imprecise probabilities, information theory, random sets and random fuzzy sets, belief functions, possibility theory, dependence modelling and copulas, clustering, depth concepts, dimensionality reduction of complex data and robustness.
Extended Abstracts Spring 2015
Extended Abstracts Spring 2015 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Extended Abstracts Spring 2015 write by Dolors Herbera. This book was released on 2016-11-30. Extended Abstracts Spring 2015 available in PDF, EPUB and Kindle. This book includes 33 expanded abstracts of selected talks given at the two workshops "Homological Bonds Between Commutative Algebra and Representation Theory" and "Brave New Algebra: Opening Perspectives," and the conference "Opening Perspectives in Algebra, Representations, and Topology," held at the Centre de Recerca Matemàtica (CRM) in Barcelona between January and June 2015. These activities were part of the one-semester intensive research program "Interactions Between Representation Theory, Algebraic Topology and Commutative Algebra (IRTATCA)." Most of the abstracts present preliminary versions of not-yet published results and cover a large number of topics (including commutative and non commutative algebra, algebraic topology, singularity theory, triangulated categories, representation theory) overlapping with homological methods. This comprehensive book is a valuable resource for the community of researchers interested in homological algebra in a broad sense, and those curious to learn the latest developments in the area. It appeals to established researchers as well as PhD and postdoctoral students who want to learn more about the latest advances in these highly active fields of research.
