Combinatorial And Toric Homotopy Introductory Lectures

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Combinatorial And Toric Homotopy: Introductory Lectures

Darby Alastair,Grbic Jelena,Lu Zhi
Combinatorial And Toric Homotopy Introductory Lectures Book PDF

Author : Darby Alastair,Grbic Jelena,Lu Zhi
Publisher : World Scientific
Page : 448 pages
File Size : 44,7 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

Combinatorial and Toric Homotopy

Alastair Darby
Combinatorial and Toric Homotopy Book PDF

Author : Alastair Darby
Publisher : Unknown
Page : 435 pages
File Size : 51,7 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.

The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles

Richard Wentworth,Graeme Wilkin
The Geometry Topology And Physics Of Moduli Spaces Of Higgs Bundles Book PDF

Author : Richard Wentworth,Graeme Wilkin
Publisher : World Scientific
Page : 412 pages
File Size : 50,8 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.

Models And Methods For Quantum Condensation And Fluids

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

Author : Weizhu Bao,Yongyong Cai,Ionut Danaila,Peter A Markowich
Publisher : World Scientific
Page : 361 pages
File Size : 42,6 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.

Genealogies of Interacting Particle Systems

Matthias Birkner,Rongfeng Sun,Jan M. Swart
Genealogies of Interacting Particle Systems Book PDF

Author : Matthias Birkner,Rongfeng Sun,Jan M. Swart
Publisher : World Scientific
Page : 363 pages
File Size : 45,9 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.

Mathematics Of Shapes And Applications

Sergey Kushnarev,Anqi Qiu,Laurent Younes
Mathematics Of Shapes And Applications Book PDF

Author : Sergey Kushnarev,Anqi Qiu,Laurent Younes
Publisher : World Scientific
Page : 220 pages
File Size : 52,7 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.

Algebraic Topology and Related Topics

Mahender Singh,Yongjin Song,Jie Wu
Algebraic Topology and Related Topics Book PDF

Author : Mahender Singh,Yongjin Song,Jie Wu
Publisher : Springer
Page : 313 pages
File Size : 44,8 Mb
Release : 2019-02-02
Category : Mathematics
ISBN : 9789811357428

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Algebraic Topology and Related Topics by Mahender Singh,Yongjin Song,Jie Wu Pdf

This book highlights the latest advances in algebraic topology, from homotopy theory, braid groups, configuration spaces and toric topology, to transformation groups and the adjoining area of knot theory. It consists of well-written original research papers and survey articles by subject experts, most of which were presented at the “7th East Asian Conference on Algebraic Topology” held at the Indian Institute of Science Education and Research (IISER), Mohali, Punjab, India, from December 1 to 6, 2017. Algebraic topology is a broad area of mathematics that has seen enormous developments over the past decade, and as such this book is a valuable resource for graduate students and researchers working in the field.

Modeling And Simulation For Collective Dynamics

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

Author : Weizhu Bao,Peter A Markowich,Benoit Perthame,Eitan Tadmor
Publisher : World Scientific
Page : 243 pages
File Size : 51,5 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.

Density Functionals For Many-particle Systems: Mathematical Theory And Physical Applications Of Effective Equations

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

Author : Berthold-georg Englert,Heinz Siedentop,Martin-isbjorn Trappe
Publisher : World Scientific
Page : 397 pages
File Size : 54,9 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.

On The Langlands Program: Endoscopy And Beyond

Wee Teck Gan,Dihua Jiang,Lei Zhang,Chen-bo Zhu
On The Langlands Program Endoscopy And Beyond Book PDF

Author : Wee Teck Gan,Dihua Jiang,Lei Zhang,Chen-bo Zhu
Publisher : World Scientific
Page : 449 pages
File Size : 43,6 Mb
Release : 2024-04-15
Category : Mathematics
ISBN : 9789811285837

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On The Langlands Program: Endoscopy And Beyond by Wee Teck Gan,Dihua Jiang,Lei Zhang,Chen-bo Zhu Pdf

This is a collection of lecture notes from the minicourses in the December 2018 Langlands Workshop: Endoscopy and Beyond. The volume combines seven introductory chapters on trace formulas, local Arthur packets, and beyond endoscopy. It aims to introduce the endoscopy classification via a basic example of the trace formula for SL(2), explore the more refined questions on the structure of Arthur packets, and look beyond endoscopy following the suggestions of Langlands, Braverman-Kazhdan, Ngo, and Altuğ. The book is a helpful reference for undergraduates, postgraduates, and researchers.

Aspects Of Computation And Automata Theory With Applications

Noam Greenberg,Sanjay Jain,Keng Meng Ng,Sven Schewe,Frank Stephan,Guohua Wu,Yue Yang
Aspects Of Computation And Automata Theory With Applications Book PDF

Author : Noam Greenberg,Sanjay Jain,Keng Meng Ng,Sven Schewe,Frank Stephan,Guohua Wu,Yue Yang
Publisher : World Scientific
Page : 492 pages
File Size : 54,9 Mb
Release : 2023-10-23
Category : Mathematics
ISBN : 9789811278648

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Aspects Of Computation And Automata Theory With Applications by Noam Greenberg,Sanjay Jain,Keng Meng Ng,Sven Schewe,Frank Stephan,Guohua Wu,Yue Yang Pdf

This volume results from two programs that took place at the Institute for Mathematical Sciences at the National University of Singapore: Aspects of Computation — in Celebration of the Research Work of Professor Rod Downey (21 August to 15 September 2017) and Automata Theory and Applications: Games, Learning and Structures (20-24 September 2021).The first program was dedicated to the research work of Rodney G. Downey, in celebration of his 60th birthday. The second program covered automata theory whereby researchers investigate the other end of computation, namely the computation with finite automata, and the intermediate level of languages in the Chomsky hierarchy (like context-free and context-sensitive languages).This volume contains 17 contributions reflecting the current state-of-art in the fields of the two programs.

Introduction to Combinatorial Torsions

Vladimir Turaev
Introduction to Combinatorial Torsions Book PDF

Author : Vladimir Turaev
Publisher : Springer Science & Business Media
Page : 140 pages
File Size : 44,8 Mb
Release : 2001-01-01
Category : Mathematics
ISBN : 3764364033

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Introduction to Combinatorial Torsions by Vladimir Turaev Pdf

This book is an introduction to combinatorial torsions of cellular spaces and manifolds with special emphasis on torsions of 3-dimensional manifolds. The first two chapters cover algebraic foundations of the theory of torsions and various topological constructions of torsions due to K. Reidemeister, J.H.C. Whitehead, J. Milnor and the author. We also discuss connections between the torsions and the Alexander polynomials of links and 3-manifolds. The third (and last) chapter of the book deals with so-called refined torsions and the related additional structures on manifolds, specifically homological orientations and Euler structures. As an application, we give a construction of the multivariable Conway polynomial of links in homology 3-spheres. At the end of the book, we briefly describe the recent results of G. Meng, C.H. Taubes and the author on the connections between the refined torsions and the Seiberg-Witten invariant of 3-manifolds. The exposition is aimed at students, professional mathematicians and physicists interested in combinatorial aspects of topology and/or in low dimensional topology. The necessary background for the reader includes the elementary basics of topology and homological algebra.

Combinatorial Homotopy and 4-dimensional Complexes

Hans J. Baues
Combinatorial Homotopy and 4 dimensional Complexes Book PDF

Author : Hans J. Baues
Publisher : Walter de Gruyter
Page : 412 pages
File Size : 49,8 Mb
Release : 1991
Category : Mathematics
ISBN : 3110124882

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Combinatorial Homotopy and 4-dimensional Complexes by Hans J. Baues Pdf

The bulk of the book is devoted to the algebraic theory of quadratic modules and their connections with 4-dimensional complexes, Pontrjagin squares, homotopy groups, the cohomology of categories, and algebraic K-theory. The first three chapters provide the background needed and may serve as an introduction to basic combinatorial homotopy theory. Annotation copyrighted by Book News, Inc., Portland, OR

Lectures on Homotopy Theory

R.A. Piccinini
Lectures on Homotopy Theory Book PDF

Author : R.A. Piccinini
Publisher : Elsevier
Page : 292 pages
File Size : 42,5 Mb
Release : 1992-01-21
Category : Mathematics
ISBN : 0080872824

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Lectures on Homotopy Theory by R.A. Piccinini Pdf

The central idea of the lecture course which gave birth to this book was to define the homotopy groups of a space and then give all the machinery needed to prove in detail that the nth homotopy group of the sphere Sn, for n greater than or equal to 1 is isomorphic to the group of the integers, that the lower homotopy groups of Sn are trivial and that the third homotopy group of S2 is also isomorphic to the group of the integers. All this was achieved by discussing H-spaces and CoH-spaces, fibrations and cofibrations (rather thoroughly), simplicial structures and the homotopy groups of maps. Later, the book was expanded to introduce CW-complexes and their homotopy groups, to construct a special class of CW-complexes (the Eilenberg-Mac Lane spaces) and to include a chapter devoted to the study of the action of the fundamental group on the higher homotopy groups and the study of fibrations in the context of a category in which the fibres are forced to live; the final material of that chapter is a comparison of various kinds of universal fibrations. Completing the book are two appendices on compactly generated spaces and the theory of colimits. The book does not require any prior knowledge of Algebraic Topology and only rudimentary concepts of Category Theory are necessary; however, the student is supposed to be well at ease with the main general theorems of Topology and have a reasonable mathematical maturity.

Toric Topology

International Conference on Toric Topology
Toric Topology Book PDF

Author : International Conference on Toric Topology
Publisher : American Mathematical Soc.
Page : 424 pages
File Size : 54,6 Mb
Release : 2008
Category : Topology
ISBN : 9780821844861

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Toric Topology by International Conference on Toric Topology 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.