Compactifications Configurations And Cohomology

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Compactifications, Configurations, and Cohomology

Peter Crooks,Alexandru I. Suciu
Compactifications Configurations and Cohomology Book PDF

Author : Peter Crooks,Alexandru I. Suciu
Publisher : American Mathematical Society
Page : 168 pages
File Size : 53,5 Mb
Release : 2023-09-25
Category : Mathematics
ISBN : 9781470469924

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Compactifications, Configurations, and Cohomology by Peter Crooks,Alexandru I. Suciu Pdf

This volume contains the proceedings of the Conference on Compactifications, Configurations, and Cohomology, held from October 22–24, 2021, at Northeastern University, Boston, MA. Some of the most active and fruitful mathematical research occurs at the interface of algebraic geometry, representation theory, and topology. Noteworthy examples include the study of compactifications in three specific settings—algebraic group actions, configuration spaces, and hyperplane arrangements. These three types of compactifications enjoy common structural features, including relations to root systems, combinatorial descriptions of cohomology rings, the appearance of iterated blow-ups, the geometry of normal crossing divisors, and connections to mirror symmetry in physics. On the other hand, these compactifications are often studied independently of one another. The articles focus on new and existing connections between the aforementioned three types of compactifications, thereby setting the stage for further research. It draws on the discipline-specific expertise of all contributors, and at the same time gives a unified, self-contained reference for compactifications and related constructions in different contexts.

Equivariant Cohomology of Configuration Spaces Mod 2

Pavle V. M. Blagojević,Frederick R. Cohen,Michael C. Crabb,Wolfgang Lück,Günter M. Ziegler
Equivariant Cohomology of Configuration Spaces Mod 2 Book PDF

Author : Pavle V. M. Blagojević,Frederick R. Cohen,Michael C. Crabb,Wolfgang Lück,Günter M. Ziegler
Publisher : Springer Nature
Page : 217 pages
File Size : 50,7 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9783030841386

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Equivariant Cohomology of Configuration Spaces Mod 2 by Pavle V. M. Blagojević,Frederick R. Cohen,Michael C. Crabb,Wolfgang Lück,Günter M. Ziegler Pdf

This book gives a brief treatment of the equivariant cohomology of the classical configuration space F(R^d,n) from its beginnings to recent developments. This subject has been studied intensively, starting with the classical papers of Artin (1925/1947) on the theory of braids, and progressing through the work of Fox and Neuwirth (1962), Fadell and Neuwirth (1962), and Arnol'd (1969). The focus of this book is on the mod 2 equivariant cohomology algebras of F(R^d,n), whose additive structure was described by Cohen (1976) and whose algebra structure was studied in an influential paper by Hung (1990). A detailed new proof of Hung's main theorem is given, however it is shown that some of the arguments given by him on the way to his result are incorrect, as are some of the intermediate results in his paper. This invalidates a paper by three of the authors, Blagojević, Lück and Ziegler (2016), who used a claimed intermediate result in order to derive lower bounds for the existence of k-regular and l-skew embeddings. Using the new proof of Hung's main theorem, new lower bounds for the existence of highly regular embeddings are obtained: Some of them agree with the previously claimed bounds, some are weaker. Assuming only a standard graduate background in algebraic topology, this book carefully guides the reader on the way into the subject. It is aimed at graduate students and researchers interested in the development of algebraic topology in its applications in geometry.

Compactifications of Symmetric and Locally Symmetric Spaces

Armand Borel,Lizhen Ji
Compactifications of Symmetric and Locally Symmetric Spaces Book PDF

Author : Armand Borel,Lizhen Ji
Publisher : Springer Science & Business Media
Page : 477 pages
File Size : 51,8 Mb
Release : 2006-07-25
Category : Mathematics
ISBN : 9780817644666

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Compactifications of Symmetric and Locally Symmetric Spaces by Armand Borel,Lizhen Ji Pdf

Introduces uniform constructions of most of the known compactifications of symmetric and locally symmetric spaces, with emphasis on their geometric and topological structures Relatively self-contained reference aimed at graduate students and research mathematicians interested in the applications of Lie theory and representation theory to analysis, number theory, algebraic geometry and algebraic topology

Algebraic and Topological Aspects of Representation Theory

Mee Seong Im,Bach Nguyen,Arik Wilbert
Algebraic and Topological Aspects of Representation Theory Book PDF

Author : Mee Seong Im,Bach Nguyen,Arik Wilbert
Publisher : American Mathematical Society
Page : 240 pages
File Size : 46,6 Mb
Release : 2024-01-22
Category : Mathematics
ISBN : 9781470470340

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Algebraic and Topological Aspects of Representation Theory by Mee Seong Im,Bach Nguyen,Arik Wilbert Pdf

This volume contains the proceedings of the virtual AMS Special Session on Geometric and Algebraic Aspects of Quantum Groups and Related Topics, held from November 20–21, 2021. Noncommutative algebras and noncommutative algebraic geometry have been an active field of research for the past several decades, with many important applications in mathematical physics, representation theory, number theory, combinatorics, geometry, low-dimensional topology, and category theory. Papers in this volume contain original research, written by speakers and their collaborators. Many papers also discuss new concepts with detailed examples and current trends with novel and important results, all of which are invaluable contributions to the mathematics community.

Mathematical Analyses of Decisions, Voting and Games

Michael A. Jones,David McCune,Jennifer M. Wilson
Mathematical Analyses of Decisions Voting and Games Book PDF

Author : Michael A. Jones,David McCune,Jennifer M. Wilson
Publisher : American Mathematical Society
Page : 210 pages
File Size : 49,5 Mb
Release : 2024-03-25
Category : Mathematics
ISBN : 9781470469788

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Mathematical Analyses of Decisions, Voting and Games by Michael A. Jones,David McCune,Jennifer M. Wilson Pdf

This volume contains the proceedings of the virtual AMS Special Session on Mathematics of Decisions, Elections and Games, held on April 8, 2022. Decision theory, voting theory, and game theory are three related areas of mathematics that involve making optimal decisions in different contexts. While these three areas are distinct, much of the recent research in these fields borrows techniques from other branches of mathematics such as algebra, combinatorics, convex geometry, logic, representation theory, etc. The papers in this volume demonstrate how the mathematics of decisions, elections, and games can be used to analyze problems from the social sciences.

Recent Developments in Fractal Geometry and Dynamical Systems

Sangita Jha,Mrinal Kanti Roychowdhury,Saurabh Verma
Recent Developments in Fractal Geometry and Dynamical Systems Book PDF

Author : Sangita Jha,Mrinal Kanti Roychowdhury,Saurabh Verma
Publisher : American Mathematical Society
Page : 270 pages
File Size : 46,8 Mb
Release : 2024-04-18
Category : Mathematics
ISBN : 9781470472160

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Recent Developments in Fractal Geometry and Dynamical Systems by Sangita Jha,Mrinal Kanti Roychowdhury,Saurabh Verma Pdf

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.

Recent Advances in Diffeologies and Their Applications

Jean-Pierre Magnot
Recent Advances in Diffeologies and Their Applications Book PDF

Author : Jean-Pierre Magnot
Publisher : American Mathematical Society
Page : 272 pages
File Size : 46,8 Mb
Release : 2024-02-02
Category : Mathematics
ISBN : 9781470472542

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Recent Advances in Diffeologies and Their Applications by Jean-Pierre Magnot Pdf

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

K. A. Brown,T. J. Hodges,M. Vancliff,J. J. Zhang
Recent Advances in Noncommutative Algebra and Geometry Book PDF

Author : K. A. Brown,T. J. Hodges,M. Vancliff,J. J. Zhang
Publisher : American Mathematical Society
Page : 288 pages
File Size : 49,8 Mb
Release : 2024-05-30
Category : Mathematics
ISBN : 9781470472399

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Recent Advances in Noncommutative Algebra and Geometry by K. A. Brown,T. J. Hodges,M. Vancliff,J. J. Zhang Pdf

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.

Advances in Functional Analysis and Operator Theory

Marat V. Markin,Igor V. Nikolaev,Carsten Trunk
Advances in Functional Analysis and Operator Theory Book PDF

Author : Marat V. Markin,Igor V. Nikolaev,Carsten Trunk
Publisher : American Mathematical Society
Page : 250 pages
File Size : 55,5 Mb
Release : 2024-04-09
Category : Mathematics
ISBN : 9781470473051

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Advances in Functional Analysis and Operator Theory by Marat V. Markin,Igor V. Nikolaev,Carsten Trunk Pdf

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.

Cohomology of the Moduli Space of Cubic Threefolds and Its Smooth Models

Sebastian Casalaina-Martin,Samuel Grushevsky,Klaus Hulek,Radu Laza
Cohomology of the Moduli Space of Cubic Threefolds and Its Smooth Models Book PDF

Author : Sebastian Casalaina-Martin,Samuel Grushevsky,Klaus Hulek,Radu Laza
Publisher : American Mathematical Society
Page : 112 pages
File Size : 42,5 Mb
Release : 2023-02-13
Category : Mathematics
ISBN : 9781470460204

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Cohomology of the Moduli Space of Cubic Threefolds and Its Smooth Models by Sebastian Casalaina-Martin,Samuel Grushevsky,Klaus Hulek,Radu Laza Pdf

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Configuration Spaces

Anders Björner,Fred Cohen,Corrado De Concini,Claudo Procesi,Mario Salvetti
Configuration Spaces Book PDF

Author : Anders Björner,Fred Cohen,Corrado De Concini,Claudo Procesi,Mario Salvetti
Publisher : Springer
Page : 547 pages
File Size : 42,7 Mb
Release : 2013-12-18
Category : Mathematics
ISBN : 9788876424311

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Configuration Spaces by Anders Björner,Fred Cohen,Corrado De Concini,Claudo Procesi,Mario Salvetti Pdf

These proceedings contain the contributions of some of the participants in the "intensive research period" held at the De Giorgi Research Center in Pisa, during the period May-June 2010. The central theme of this research period was the study of configuration spaces from various points of view. This topic originated from the intersection of several classical theories: Braid groups and related topics, configurations of vectors (of great importance in Lie theory and representation theory), arrangements of hyperplanes and of subspaces, combinatorics, singularity theory. Recently, however, configuration spaces have acquired independent interest and indeed the contributions in this volume go far beyond the above subjects, making it attractive to a large audience of mathematicians.

Cohomology of the Moduli Space of Cubic Threefolds and Its Smooth Models

Sebastian Casalaina-Martin,Samuel Grushevsky,Klaus Hulek,Radu Laza
Cohomology of the Moduli Space of Cubic Threefolds and Its Smooth Models Book PDF

Author : Sebastian Casalaina-Martin,Samuel Grushevsky,Klaus Hulek,Radu Laza
Publisher : Unknown
Page : 0 pages
File Size : 49,7 Mb
Release : 2023
Category : Cohomology operations
ISBN : 1470473518

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Cohomology of the Moduli Space of Cubic Threefolds and Its Smooth Models by Sebastian Casalaina-Martin,Samuel Grushevsky,Klaus Hulek,Radu Laza Pdf

"We compute and compare the (intersection) cohomology of various natural geometric compactifications of the moduli space of cubic threefolds: the GIT compactification and its Kirwan blowup, as well as the Baily-Borel and toroidal compactifications of the ball quotient model, due to Allcock-Carlson-Toledo. Our starting point is Kirwan's method. We then follow by investigating the behavior of the cohomology under the birational maps relating the various models, using the decomposition theorem in different ways, and via a detailed study of the boundary of the ball quotient model. As an easy illustration of our methods, the simpler case of the moduli space of cubic surfaces is discussed in an appendix."--Page v.

Compactifications of Symmetric Spaces

Yves Guivarc'h,Lizhen Ji,John C. Taylor
Compactifications of Symmetric Spaces Book PDF

Author : Yves Guivarc'h,Lizhen Ji,John C. Taylor
Publisher : Springer Science & Business Media
Page : 297 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461224525

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Compactifications of Symmetric Spaces by Yves Guivarc'h,Lizhen Ji,John C. Taylor Pdf

The concept of symmetric space is of central importance in many branches of mathematics. Compactifications of these spaces have been studied from the points of view of representation theory, geometry, and random walks. This work is devoted to the study of the interrelationships among these various compactifications and, in particular, focuses on the martin compactifications. It is the first exposition to treat compactifications of symmetric spaces systematically and to uniformized the various points of view. The work is largely self-contained, with comprehensive references to the literature. It is an excellent resource for both researchers and graduate students.

Quantum Cohomology

K. Behrend,C. Gomez,V. Tarasov,G. Tian
Quantum Cohomology Book PDF

Author : K. Behrend,C. Gomez,V. Tarasov,G. Tian
Publisher : Springer
Page : 322 pages
File Size : 40,7 Mb
Release : 2004-10-14
Category : Mathematics
ISBN : 9783540456179

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Quantum Cohomology by K. Behrend,C. Gomez,V. Tarasov,G. Tian Pdf

The book gathers the lectures given at the C.I.M.E. summer school "Quantum Cohomology" held in Cetraro (Italy) from June 30th to July 8th, 1997. The lectures and the subsequent updating cover a large spectrum of the subject on the field, from the algebro-geometric point of view, to the symplectic approach, including recent developments of string-branes theories and q-hypergeometric functions.

String Theory Compactifications

Mariana Graña,Hagen Triendl
String Theory Compactifications Book PDF

Author : Mariana Graña,Hagen Triendl
Publisher : Springer
Page : 74 pages
File Size : 55,5 Mb
Release : 2017-03-21
Category : Science
ISBN : 9783319543161

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String Theory Compactifications by Mariana Graña,Hagen Triendl Pdf

The lectures in this book provide graduate students and non-specialist researchers with a concise introduction to the concepts and formalism required to reduce the ten-dimensional string theories to the observable four-dimensional space-time - a procedure called string compactification. The text starts with a very brief introduction to string theory, first working out its massless spectrum and showing how the condition on the number of dimensions arises. It then dwells on the different possible internal manifolds, from the simplest to the most relevant phenomenologically, thereby showing that the most elegant description is through an extension of ordinary Riemannian geometry termed generalized geometry, which was first introduced by Hitchin. Last but not least, the authors review open problems in string phenomenology, such as the embedding of the Standard Model and obtaining de Sitter solutions.