› › Recent Advances In Diffeologies And Their Applications

Recent Advances in Diffeologies and Their Applications

Author : Jean-Pierre Magnot

Publisher : American Mathematical Society

Page : 272 pages

File Size : 20,25 MB

Release : 2024-02-02

Category : Mathematics

ISBN : 1470472546

Get eBook

Book Description

This volume contains the proceedings of the AMS-EMS-SMF Special Session on Recent Advances in Diffeologies and Their Applications, held from July 18–20, 2022, at the Université de Grenoble-Alpes, Grenoble, France. The articles present some developments of the theory of diffeologies applied in a broad range of topics, ranging from algebraic topology and higher homotopy theory to integrable systems and optimization in PDE. The geometric framework proposed by diffeologies is known to be one of the most general approaches to problems arising in several areas of mathematics. It can adapt to many contexts without major technical difficulties and produce examples inaccessible by other means, in particular when studying singularities or geometry in infinite dimension. Thanks to this adaptability, diffeologies appear to have become an interesting and useful language for a growing number of mathematicians working in many different fields. Some articles in the volume also illustrate some recent developments of the theory, which makes it even more deep and useful.



Recent Advances in Noncommutative Algebra and Geometry

Author : K. A. Brown

Publisher : American Mathematical Society

Page : 288 pages

File Size : 37,87 MB

Release : 2024-05-30

Category : Mathematics

ISBN : 1470472392

Get eBook

Book Description

This volume contains the proceedings of the conference Recent Advances and New Directions in the Interplay of Noncommutative Algebra and Geometry, held from June 20–24, 2022, at the University of Washington, Seattle, in honor of S. Paul Smith's 65th birthday. The articles reflect the wide interests of Smith and provide researchers and graduate students with an indispensable overview of topics of current interest. Specific fields covered include: noncommutative algebraic geometry, representation theory, Hopf algebras and quantum groups, the elliptic algebras of Feigin and Odesskii, Calabi-Yau algebras, Artin-Schelter regular algebras, deformation theory, and Lie theory. In addition to original research contributions the volume includes an introductory essay reviewing Smith's research contributions in these fields, and several survey articles.



Recent Developments in Fractal Geometry and Dynamical Systems

Author : Sangita Jha

Publisher : American Mathematical Society

Page : 270 pages

File Size : 13,83 MB

Release : 2024-04-18

Category : Mathematics

ISBN : 1470472163

Get eBook

Book Description

This volume contains the proceedings of the virtual AMS Special Session on Fractal Geometry and Dynamical Systems, held from May 14–15, 2022. The content covers a wide range of topics. It includes nonautonomous dynamics of complex polynomials, theory and applications of polymorphisms, topological and geometric problems related to dynamical systems, and also covers fractal dimensions, including the Hausdorff dimension of fractal interpolation functions. Furthermore, the book contains a discussion of self-similar measures as well as the theory of IFS measures associated with Bratteli diagrams. This book is suitable for graduate students interested in fractal theory, researchers interested in fractal geometry and dynamical systems, and anyone interested in the application of fractals in science and engineering. This book also offers a valuable resource for researchers working on applications of fractals in different fields.



Advances in Functional Analysis and Operator Theory

Author : Marat V. Markin

Publisher : American Mathematical Society

Page : 250 pages

File Size : 20,36 MB

Release : 2024-04-09

Category : Mathematics

ISBN : 1470473054

Get eBook

Book Description

This volume contains the proceedings of the AMS-EMS-SMF Special Session on Advances in Functional Analysis and Operator Theory, held July 18–22, 2022, at the Université de Grenoble-Alpes, Grenoble, France. The papers reflect the modern interplay between differential equations, functional analysis, operator algebras, and their applications from the dynamics to quantum groups to number theory. Among the topics discussed are the Sturm-Liouville and boundary value problems, axioms of quantum mechanics, $C^{*}$-algebras and symbolic dynamics, von Neumann algebras and low-dimensional topology, quantum permutation groups, the Jordan algebras, and the Kadison–Singer transforms.



Moduli Spaces and Vector Bundles—New Trends

Author : Peter Gothen

Publisher : American Mathematical Society

Page : 382 pages

File Size : 31,47 MB

Release : 2024-07-18

Category : Mathematics

ISBN : 1470472961

Get eBook

Book Description

This volume contains the proceedings of the VBAC 2022 Conference on Moduli Spaces and Vector Bundles—New Trends, held in honor of Peter Newstead's 80th birthday, from July 25–29, 2022, at the University of Warwick, Coventry, United Kingdom. The papers focus on the theory of stability conditions in derived categories, non-reductive geometric invariant theory, Brill-Noether theory, and Higgs bundles and character varieties. The volume includes both survey and original research articles. Most articles contain substantial background and will be helpful to both novices and experts.



A Glimpse into Geometric Representation Theory

Author : Mahir Bilen Can

Publisher : American Mathematical Society

Page : 218 pages

File Size : 26,56 MB

Release : 2024-08-07

Category : Mathematics

ISBN : 147047090X

Get eBook

Book Description

This volume contains the proceedings of the AMS Special Session on Combinatorial and Geometric Representation Theory, held virtually on November 20–21, 2021. The articles offer an engaging look into recent advancements in geometric representation theory. Despite diverse subject matters, a common thread uniting the articles of this volume is the power of geometric methods. The authors explore the following five contemporary topics in geometric representation theory: equivariant motivic Chern classes; equivariant Hirzebruch classes and equivariant Chern-Schwartz-MacPherson classes of Schubert cells; locally semialgebraic spaces, Nash manifolds, and their superspace counterparts; support varieties of Lie superalgebras; wreath Macdonald polynomials; and equivariant extensions and solutions of the Deligne-Simpson problem. Each article provides a well-structured overview of its topic, highlighting the emerging theories developed by the authors and their colleagues.



Higher Structures in Topology, Geometry, and Physics

Author : Ralph M. Kaufmann

Publisher : American Mathematical Society

Page : 332 pages

File Size : 50,24 MB

Release : 2024-07-03

Category : Mathematics

ISBN : 1470471426

Get eBook

Book Description

This volume contains the proceedings of the AMS Special Session on Higher Structures in Topology, Geometry, and Physics, held virtually on March 26–27, 2022. The articles give a snapshot survey of the current topics surrounding the mathematical formulation of field theories. There is an intricate interplay between geometry, topology, and algebra which captures these theories. The hallmark are higher structures, which one can consider as the secondary algebraic or geometric background on which the theories are formulated. The higher structures considered in the volume are generalizations of operads, models for conformal field theories, string topology, open/closed field theories, BF/BV formalism, actions on Hochschild complexes and related complexes, and their geometric and topological aspects.



Deformation of Artinian Algebras and Jordan Type

Author : Anthony Iarrobino

Publisher : American Mathematical Society

Page : 254 pages

File Size : 26,78 MB

Release : 2024-09-06

Category : Mathematics

ISBN : 1470473569

Get eBook

Book Description

This volume contains the proceedings of the AMS-EMS-SMF Special Session on Deformations of Artinian Algebras and Jordan Type, held July 18?22, 2022, at the Universit‚ Grenoble Alpes, Grenoble, France. Articles included are a survey and open problems on deformations and relation to the Hilbert scheme; a survey of commuting nilpotent matrices and their Jordan type; and a survey of Specht ideals and their perfection in the two-rowed case. Other articles treat topics such as the Jordan type of local Artinian algebras, Waring decompositions of ternary forms, questions about Hessians, a geometric approach to Lefschetz properties, deformations of codimension two local Artin rings using Hilbert-Burch matrices, and parametrization of local Artinian algebras in codimension three. Each of the articles brings new results on the boundary of commutative algebra and algebraic geometry.



Diffeology

Author : Patrick Iglesias-Zemmour

Publisher : American Mathematical Soc.

Page : 467 pages

File Size : 30,58 MB

Release : 2013-04-09

Category : Mathematics

ISBN : 0821891316

Get eBook

Book Description

Diffeology is an extension of differential geometry. With a minimal set of axioms, diffeology allows us to deal simply but rigorously with objects which do not fall within the usual field of differential geometry: quotients of manifolds (even non-Hausdorff), spaces of functions, groups of diffeomorphisms, etc. The category of diffeology objects is stable under standard set-theoretic operations, such as quotients, products, co-products, subsets, limits, and co-limits. With its right balance between rigor and simplicity, diffeology can be a good framework for many problems that appear in various areas of physics. Actually, the book lays the foundations of the main fields of differential geometry used in theoretical physics: differentiability, Cartan differential calculus, homology and cohomology, diffeological groups, fiber bundles, and connections. The book ends with an open program on symplectic diffeology, a rich field of application of the theory. Many exercises with solutions make this book appropriate for learning the subject.



Towards the Mathematics of Quantum Field Theory

Author : Frédéric Paugam

Publisher : Springer Science & Business Media

Page : 485 pages

File Size : 46,39 MB

Release : 2014-02-20

Category : Science

ISBN : 3319045644

Get eBook

Book Description

This ambitious and original book sets out to introduce to mathematicians (even including graduate students ) the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of the mathematical objects in use. This in turn promotes the interaction between mathematicians and physicists by supplying a common and flexible language for the good of both communities, though mathematicians are the primary target. This reference work provides a coherent and complete mathematical toolbox for classical and quantum field theory, based on categorical and homotopical methods, representing an original contribution to the literature. The first part of the book introduces the mathematical methods needed to work with the physicists' spaces of fields, including parameterized and functional differential geometry, functorial analysis, and the homotopical geometric theory of non-linear partial differential equations, with applications to general gauge theories. The second part presents a large family of examples of classical field theories, both from experimental and theoretical physics, while the third part provides an introduction to quantum field theory, presents various renormalization methods, and discusses the quantization of factorization algebras.