Combinatorial And Toric Homotopy

Author : Darby Alastair,Grbic Jelena,Lu Zhi
Publisher : World Scientific
Page : 448 pages
File Size : 50,8 Mb
Release : 2017-10-20
Category : Mathematics
ISBN : 9789813226586

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Combinatorial And Toric Homotopy: Introductory Lectures by Darby Alastair,Grbic Jelena,Lu Zhi Pdf

This volume consists of introductory lectures on the topics in the new and rapidly developing area of toric homotopy theory, and its applications to the current research in configuration spaces and braids, as well as to more applicable mathematics such as fr-codes and robot motion planning. The book starts intertwining homotopy theoretical and combinatorial ideas within the remits of toric topology and illustrates an attempt to classify in a combinatorial way polytopes known as fullerenes, which are important objects in quantum physics, quantum chemistry and nanotechnology. Toric homotopy theory is then introduced as a further development of toric topology, which describes properties of Davis–Januszkiewicz spaces, moment-angle complexes and their generalizations to polyhedral products. The book also displays the current research on configuration spaces, braids, the theory of limits over the category of presentations and the theory of fr-codes. As an application to robotics, the book surveys topological problems relevant to the motion planning problem of robotics and includes new results and constructions, which enrich the emerging area of topological robotics. The book is at research entry level addressing the core components in homotopy theory and their important applications in the sciences and thus suitable for advanced undergraduate and graduate students. Contents: Toric Homotopy Theory (Stephen Theriault)Fullerenes, Polytopes and Toric Topology (Victor M Buchstaber and Nikolay Yu Erokhovets)Around Braids (Vladimir Vershinin)Higher Limits, Homology Theories and fr-Codes (Sergei O Ivanov and Roman Mikhailov)Configuration Spaces and Robot Motion Planning Algorithms (Michael Farber)Cellular Stratified Spaces (Dai Tamaki) Readership: Advanced undergraduate and graduate students as well as researchers interested in homotopy theory and its applications in the sciences. Keywords: Toric Topology;Toric Homotopy;Configuration Space;Stratified Spaces;Braid Group;Fullerene;Polytope;Virtual Braid Group;Thompson Group;Robotics;Motion PlanningReview: Key Features: The first book in the area of toric homotopy theory consisting of introductory lectures on the topics and their applications to fr-codes and robot motion planning

Author : Alastair Darby
Publisher : Unknown
Page : 435 pages
File Size : 52,5 Mb
Release : 2018
Category : Combinatorial topology
ISBN : 9813226579

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Combinatorial and Toric Homotopy by Alastair Darby Pdf

"This volume consists of introductory lectures on the topics in the new and rapidly developing area of toric homotopy theory, and its applications to the current research in configuration spaces and braids, as well as to more applicable mathematics such as fr-codes and robot motion planning. The book starts intertwining homotopy theoretical and combinatorial ideas within the remits of toric topology and illustrates an attempt to classify in a combinatorial way polytopes known as fullerenes, which are important objects in quantum physics, quantum chemistry and nanotechnology. Toric homotopy theory is then introduced as a further development of toric topology, which describes properties of Davis-Januszkiewicz spaces, moment-angle complexes and their generalizations to polyhedral products. The book also displays the current research on configuration spaces, braids, the theory of limits over the category of presentations and the theory of fr-codes. As an application to robotics, the book surveys topological problems relevant to the motion planning problem of robotics and includes new results and constructions, which enrich the emerging area of topological robotics. The book is at research entry level addressing the core components in homotopy theory and their important applications in the sciences and thus suitable for advanced undergraduate and graduate students."--Publisher's website.

Author : Megumi Harada
Publisher : American Mathematical Soc.
Page : 424 pages
File Size : 47,5 Mb
Release : 2008
Category : Mathematics
ISBN : 9780821844861

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Toric Topology by Megumi Harada Pdf

Toric topology is the study of algebraic, differential, symplectic-geometric, combinatorial, and homotopy-theoretic aspects of a particular class of torus actions whose quotients are highly structured. The combinatorial properties of this quotient and the equivariant topology of the original manifold interact in a rich variety of ways, thus illuminating subtle aspects of both the combinatorics and the equivariant topology. Many of the motivations and guiding principles of the fieldare provided by (though not limited to) the theory of toric varieties in algebraic geometry as well as that of symplectic toric manifolds in symplectic geometry.This volume is the proceedings of the International Conference on Toric Topology held in Osaka in May-June 2006. It contains about 25 research and survey articles written by conference speakers, covering many different aspects of, and approaches to, torus actions, such as those mentioned above. Some of the manuscripts are survey articles, intended to give a broad overview of an aspect of the subject; all manuscripts consciously aim to be accessible to a broad reading audience of students andresearchers interested in the interaction of the subjects involved. We hope that this volume serves as an enticing invitation to this emerging field.

Author : Victor M. Buchstaber,Taras E. Pano
Publisher : American Mathematical Soc.
Page : 518 pages
File Size : 50,8 Mb
Release : 2015-07-15
Category : Algebraic topology
ISBN : 9781470422141

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Toric Topology by Victor M. Buchstaber,Taras E. Pano Pdf

This book is about toric topology, a new area of mathematics that emerged at the end of the 1990s on the border of equivariant topology, algebraic and symplectic geometry, combinatorics, and commutative algebra. It has quickly grown into a very active area with many links to other areas of mathematics, and continues to attract experts from different fields. The key players in toric topology are moment-angle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of moment-angle manifolds relates to combinatorial geometry and algebraic geometry of toric varieties via the notion of a quasitoric manifold. Discovery of remarkable geometric structures on moment-angle manifolds led to important connections with classical and modern areas of symplectic, Lagrangian, and non-Kaehler complex geometry. A related categorical construction of moment-angle complexes and polyhedral products provides for a universal framework for many fundamental constructions of homotopical topology. The study of polyhedral products is now evolving into a separate subject of homotopy theory. A new perspective on torus actions has also contributed to the development of classical areas of algebraic topology, such as complex cobordism. This book includes many open problems and is addressed to experts interested in new ideas linking all the subjects involved, as well as to graduate students and young researchers ready to enter this beautiful new area.

Author : Najib Idrissi
Publisher : Springer Nature
Page : 201 pages
File Size : 48,5 Mb
Release : 2022-06-11
Category : Mathematics
ISBN : 9783031044281

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Real Homotopy of Configuration Spaces by Najib Idrissi Pdf

This volume provides a unified and accessible account of recent developments regarding the real homotopy type of configuration spaces of manifolds. Configuration spaces consist of collections of pairwise distinct points in a given manifold, the study of which is a classical topic in algebraic topology. One of this theory’s most important questions concerns homotopy invariance: if a manifold can be continuously deformed into another one, then can the configuration spaces of the first manifold be continuously deformed into the configuration spaces of the second? This conjecture remains open for simply connected closed manifolds. Here, it is proved in characteristic zero (i.e. restricted to algebrotopological invariants with real coefficients), using ideas from the theory of operads. A generalization to manifolds with boundary is then considered. Based on the work of Campos, Ducoulombier, Lambrechts, Willwacher, and the author, the book covers a vast array of topics, including rational homotopy theory, compactifications, PA forms, propagators, Kontsevich integrals, and graph complexes, and will be of interest to a wide audience.

Author : Anthony Bahri,Lisa Jeffrey,Taras Panov,Donald Stanley,Stephen Theriault
Publisher : Springer
Page : 0 pages
File Size : 51,5 Mb
Release : 2024-06-14
Category : Mathematics
ISBN : 3031572033

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Toric Topology and Polyhedral Products by Anthony Bahri,Lisa Jeffrey,Taras Panov,Donald Stanley,Stephen Theriault Pdf

This book explores toric topology, polyhedral products and related mathematics from a wide range of perspectives, collectively giving an overview of the potential of the areas while contributing original research to drive the subject forward in interesting new directions. Contributions to this volume were written in connection to the thematic program Toric Topology and Polyhedral Products held at the Fields Institute from January-June 2020. 16 original conributions were inspired or influenced by the program. Toric Topology arose as a subject in its own right about twenty-five years ago. It sits at the intersection of commutative algebra, topology, combinatorics, algebraic geometry, and symplectic and convex geometry. Polyhedral products are a functorial generalization of a construction that is at the centre of Toric Topology. They are of independent interest and unify several constructions that arise in a diverse range of areas, such as geometric group theory, homotopy theory, algebraic combinatorics and subspace arrangements.

Author : Anatoly M. Vershik,Victor M. Buchstaber,Andrey V. Malyutin
Publisher : American Mathematical Soc.
Page : 345 pages
File Size : 47,6 Mb
Release : 2021-08-30
Category : Education
ISBN : 9781470456641

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Topology, Geometry, and Dynamics: V. A. Rokhlin-Memorial by Anatoly M. Vershik,Victor M. Buchstaber,Andrey V. Malyutin Pdf

Vladimir Abramovich Rokhlin (8/23/1919–12/03/1984) was one of the leading Russian mathematicians of the second part of the twentieth century. His main achievements were in algebraic topology, real algebraic geometry, and ergodic theory. The volume contains the proceedings of the Conference on Topology, Geometry, and Dynamics: V. A. Rokhlin-100, held from August 19–23, 2019, at The Euler International Mathematics Institute and the Steklov Institute of Mathematics, St. Petersburg, Russia. The articles deal with topology of manifolds, theory of cobordisms, knot theory, geometry of real algebraic manifolds and dynamical systems and related topics. The book also contains Rokhlin's biography supplemented with copies of actual very interesting documents.

Author : Anthony Bahri
Publisher : Springer Nature
Page : 325 pages
File Size : 46,6 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9783031572043

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Toric Topology and Polyhedral Products by Anthony Bahri Pdf

Author : Alexei Skorobogatov
Publisher : Cambridge University Press
Page : 470 pages
File Size : 50,7 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9781107616127

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Torsors, Étale Homotopy and Applications to Rational Points by Alexei Skorobogatov Pdf

Lecture notes and research articles on the use of torsors and étale homotopy in algebraic and arithmetic geometry.

Author : Weizhu Bao,Yongyong Cai,Ionut Danaila,Peter A Markowich
Publisher : World Scientific
Page : 361 pages
File Size : 41,5 Mb
Release : 2023-01-04
Category : Mathematics
ISBN : 9789811266065

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Models And Methods For Quantum Condensation And Fluids by Weizhu Bao,Yongyong Cai,Ionut Danaila,Peter A Markowich Pdf

The Institute for Mathematical Sciences at the National University of Singapore hosted a thematic program on Quantum and Kinetic Problems: Modeling, Analysis, Numerics and Applications from September 2019 to March 2020. As an important part of the program, tutorials and special lectures were given by leading experts in the fields for participating graduate students and junior researchers. This invaluable volume collects six expanded lecture notes with self-contained tutorials. The coverage includes mathematical models and numerical methods for multidimensional solitons in linear and nonlinear potentials; Bose-Einstein condensation (BEC) with dipole-dipole interaction, higher order interaction and spin-orbit coupling; classical and quantum turbulence; and molecular dynamics process based on the first-principle in quantum chemistry.This volume serves to inspire graduate students and researchers who will embark into original research work in these fields.

Author : Richard Wentworth,Graeme Wilkin
Publisher : World Scientific
Page : 412 pages
File Size : 47,5 Mb
Release : 2018-06-28
Category : Mathematics
ISBN : 9789813229105

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The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles by Richard Wentworth,Graeme Wilkin Pdf

In the 25 years since their introduction, Higgs bundles have seen a surprising number of interactions within different areas of mathematics and physics. There is a recent surge of interest following Ngô Bau Châu's proof of the Fundamental Lemma and the work of Kapustin and Witten on the Geometric Langlands program. The program on The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles, was held at the Institute for Mathematical Sciences at the National University of Singapore during 2014. It hosted a number of lectures on recent topics of importance related to Higgs bundles, and it is the purpose of this volume to collect these lectures in a form accessible to graduate students and young researchers interested in learning more about this field.

Author : Matthias Birkner,Rongfeng Sun,Jan M. Swart
Publisher : World Scientific
Page : 363 pages
File Size : 45,8 Mb
Release : 2020
Category : Biomathematics
ISBN : 9789811206092

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Genealogies of Interacting Particle Systems by Matthias Birkner,Rongfeng Sun,Jan M. Swart Pdf

"Interacting particle systems are Markov processes involving infinitely many interacting components. Since their introduction in the 1970s, researchers have found many applications in statistical physics and population biology. Genealogies, which follow the origin of the state of a site backwards in time, play an important role in their studies, especially for the biologically motivated systems. The program Genealogies of Interacting Particle Systems held at the Institute for Mathematical Sciences, National University of Singapore, from 17 July to 18 Aug 2017, brought together experts and young researchers interested in this modern topic. Central to the program were learning sessions where lecturers presented work outside of their own research, as well as a normal workshop "--Publisher's website.

Author : Sergey Kushnarev,Anqi Qiu,Laurent Younes
Publisher : World Scientific
Page : 220 pages
File Size : 53,8 Mb
Release : 2019-11-20
Category : Mathematics
ISBN : 9789811200144

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Mathematics Of Shapes And Applications by Sergey Kushnarev,Anqi Qiu,Laurent Younes Pdf

Understanding how a single shape can incur a complex range of transformations, while defining the same perceptually obvious figure, entails a rich and challenging collection of problems, at the interface between applied mathematics, statistics and computer science. The program on Mathematics of Shapes and Applications, was held at the Institute for Mathematical Sciences at the National University of Singapore in 2016. It provided discussions on theoretical developments and numerous applications in computer vision, object recognition and medical imaging.The analysis of shapes is an example of a mathematical problem directly connected with applications while offering deep open challenges to theoretical mathematicians. It has grown, over the past decades, into an interdisciplinary area in which researchers studying infinite-dimensional Riemannian manifolds (global analysis) interact with applied mathematicians, statisticians, computer scientists and biomedical engineers on a variety of problems involving shapes.The volume illustrates this wealth of subjects by providing new contributions on the metric structure of diffeomorphism groups and shape spaces, recent developments on deterministic and stochastic models of shape evolution, new computational methods manipulating shapes, and new statistical tools to analyze shape datasets. In addition to these contributions, applications of shape analysis to medical imaging and computational anatomy are discussed, leading, in particular, to improved understanding of the impact of cognitive diseases on the geometry of the brain.

Author : Weizhu Bao,Peter A Markowich,Benoit Perthame,Eitan Tadmor
Publisher : World Scientific
Page : 243 pages
File Size : 55,5 Mb
Release : 2023-01-17
Category : Mathematics
ISBN : 9789811266157

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Modeling And Simulation For Collective Dynamics by Weizhu Bao,Peter A Markowich,Benoit Perthame,Eitan Tadmor Pdf

The thematic program Quantum and Kinetic Problems: Modeling, Analysis, Numerics and Applications was held at the Institute for Mathematical Sciences at the National University of Singapore, from September 2019 to March 2020. Leading experts presented tutorials and special lectures geared towards the participating graduate students and junior researchers.Readers will find in this significant volume four expanded lecture notes with self-contained tutorials on modeling and simulation for collective dynamics including individual and population approaches for population dynamics in mathematical biology, collective behaviors for Lohe type aggregation models, mean-field particle swarm optimization, and consensus-based optimization and ensemble Kalman inversion for global optimization problems with constraints.This volume serves to inspire graduate students and researchers who will embark into original research work in kinetic models for collective dynamics and their applications.

Author : Berthold-georg Englert,Heinz Siedentop,Martin-isbjorn Trappe
Publisher : World Scientific
Page : 397 pages
File Size : 40,9 Mb
Release : 2023-02-10
Category : Science
ISBN : 9789811272165

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Density Functionals For Many-particle Systems: Mathematical Theory And Physical Applications Of Effective Equations by Berthold-georg Englert,Heinz Siedentop,Martin-isbjorn Trappe Pdf

Density Functional Theory (DFT) first established it's theoretical footing in the 1960s from the framework of Hohenberg-Kohn theorems. DFT has since seen much development in evaluation techniques as well as application in solving problems in Physics, Mathematics and Chemistry.This review volume, part of the IMS Lecture Notes Series, is a collection of contributions from the September 2019 Workshop on the topic, held in the Institute for Mathematical Sciences, National University of Singapore.With contributions from prominent Mathematicians, Physicists, and Chemists, the volume is a blend of comprehensive review articles on the Mathematical and the Physicochemical aspects of DFT and shorter contributions on particular themes, including numerical implementations.The book will be a useful reference for advanced undergraduate and postgraduate students as well as researchers.