The Geometry Topology And Physics Of Moduli Spaces Of Higgs Bundles
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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.
Moduli Spaces And Vector Bundles
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Author : Leticia Brambila-Paz
language : en
Publisher: Cambridge University Press
Release Date : 2009-05-21
Moduli Spaces And Vector Bundles written by Leticia Brambila-Paz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-21 with Mathematics categories.
Vector bundles and their associated moduli spaces are of fundamental importance in algebraic geometry. In recent decades this subject has been greatly enhanced by its relationships with other areas of mathematics, including differential geometry, topology and even theoretical physics, specifically gauge theory, quantum field theory and string theory. Peter E. Newstead has been a leading figure in this field almost from its inception and has made many seminal contributions to our understanding of moduli spaces of stable bundles. This volume has been assembled in tribute to Professor Newstead and his contribution to algebraic geometry. Some of the subject's leading experts cover foundational material, while the survey and research papers focus on topics at the forefront of the field. This volume is suitable for both graduate students and more experienced researchers.
Moduli Spaces
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Author : Leticia Brambila
language : en
Publisher: Cambridge University Press
Release Date : 2014-03-13
Moduli Spaces written by Leticia Brambila and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-13 with Mathematics categories.
A graduate-level introduction to some of the important contemporary ideas and problems in the theory of moduli spaces.
Geometric Invariant Theory Holomorphic Vector Bundles And The Harder Narasimhan Filtration
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Author : Alfonso Zamora Saiz
language : en
Publisher: Springer Nature
Release Date : 2021-03-24
Geometric Invariant Theory Holomorphic Vector Bundles And The Harder Narasimhan Filtration written by Alfonso Zamora Saiz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-24 with Mathematics categories.
This book introduces key topics on Geometric Invariant Theory, a technique to obtaining quotients in algebraic geometry with a good set of properties, through various examples. It starts from the classical Hilbert classification of binary forms, advancing to the construction of the moduli space of semistable holomorphic vector bundles, and to Hitchin’s theory on Higgs bundles. The relationship between the notion of stability between algebraic, differential and symplectic geometry settings is also covered. Unstable objects in moduli problems -- a result of the construction of moduli spaces -- get specific attention in this work. The notion of the Harder-Narasimhan filtration as a tool to handle them, and its relationship with GIT quotients, provide instigating new calculations in several problems. Applications include a survey of research results on correspondences between Harder-Narasimhan filtrations with the GIT picture and stratifications of the moduli space of Higgs bundles. Graduate students and researchers who want to approach Geometric Invariant Theory in moduli constructions can greatly benefit from this reading, whose key prerequisites are general courses on algebraic geometry and differential geometry.
Integrable Systems
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Author : N.J. Hitchin
language : en
Publisher: Oxford University Press, USA
Release Date : 2013-03-14
Integrable Systems written by N.J. Hitchin and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors, this book has its origins in a lecture series given by the internationally renowned authors. Written in an accessible, informal style, it fills a gap in the existing literature.
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.
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.
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.
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.