Combinatorial And Toric Homotopy Introductory Lectures
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Combinatorial And Toric Homotopy Introductory Lectures
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Author : Alastair Darby
language : en
Publisher: World Scientific
Release Date : 2017-10-20
Combinatorial And Toric Homotopy Introductory Lectures written by Alastair Darby and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-20 with Mathematics categories.
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.
The Geometry Topology And Physics Of Moduli Spaces Of Higgs Bundles
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Author : Richard Wentworth
language : en
Publisher: World Scientific
Release Date : 2018-06-28
The Geometry Topology And Physics Of Moduli Spaces Of Higgs Bundles written by Richard Wentworth and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-28 with Mathematics categories.
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
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Author : Weizhu Bao
language : en
Publisher: World Scientific
Release Date : 2023-01-04
Models And Methods For Quantum Condensation And Fluids written by Weizhu Bao and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-04 with Mathematics categories.
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
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Author : Matthias Birkner
language : en
Publisher: World Scientific
Release Date : 2020
Genealogies Of Interacting Particle Systems written by Matthias Birkner and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Biomathematics categories.
"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
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Author : Sergey Kushnarev
language : en
Publisher: World Scientific
Release Date : 2019-11-20
Mathematics Of Shapes And Applications written by Sergey Kushnarev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-20 with Mathematics categories.
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.
Density Functionals For Many Particle Systems Mathematical Theory And Physical Applications Of Effective Equations
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Author : Berthold-georg Englert
language : en
Publisher: World Scientific
Release Date : 2023-02-10
Density Functionals For Many Particle Systems Mathematical Theory And Physical Applications Of Effective Equations written by Berthold-georg Englert and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-10 with Science categories.
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.
Aspects Of Computation And Automata Theory With Applications
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Author : Noam Greenberg
language : en
Publisher: World Scientific
Release Date : 2023-10-23
Aspects Of Computation And Automata Theory With Applications written by Noam Greenberg and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-23 with Mathematics categories.
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.
On The Langlands Program Endoscopy And Beyond
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Author : Wee Teck Gan
language : en
Publisher: World Scientific
Release Date : 2024-04-15
On The Langlands Program Endoscopy And Beyond written by Wee Teck Gan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-15 with Mathematics categories.
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.
Higher Recursion Theory And Set Theory
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Author : James Cummings
language : en
Publisher: World Scientific
Release Date : 2025-02-18
Higher Recursion Theory And Set Theory written by James Cummings and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-18 with Mathematics categories.
This volume celebrates the research contributions of Professors Theodore A Slaman and W Hugh Woodin, marking their distinguished careers in higher recursion theory and set theory as they approached the milestone of their 65th birthdays in 2019. It originates from the Institute for Mathematical Sciences program, Higher Recursion Theory and Set Theory, held at the National University of Singapore (May 20-June 14, 2019).The program explored cutting-edge developments in higher recursion theory, set theory, and their intricate interconnections. Topics discussed during the workshop included Martin's conjecture, higher randomness, the HOD conjecture, descriptive inner model theory, and the Ultimate-L program.This volume presents 15 peer-reviewed contributions by leading experts in the field, offering a comprehensive overview of recent advances in higher recursion theory and set theory, with a focus on their dynamic interactions.
Modeling And Simulation For Collective Dynamics
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Author : Weizhu Bao
language : en
Publisher: World Scientific
Release Date : 2023-01-17
Modeling And Simulation For Collective Dynamics written by Weizhu Bao and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-17 with Mathematics categories.
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.