Forcing Iterated Ultrapowers And Turing Degrees

Author : Chitat Chong,Qi Feng,Theodore A Slaman,W Hugh Woodin,Yue Yang
Publisher : World Scientific
Page : 184 pages
File Size : 55,8 Mb
Release : 2015-07-30
Category : Mathematics
ISBN : 9789814699969

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Forcing, Iterated Ultrapowers, and Turing Degrees by Chitat Chong,Qi Feng,Theodore A Slaman,W Hugh Woodin,Yue Yang Pdf

This volume presents the lecture notes of short courses given by three leading experts in mathematical logic at the 2010 and 2011 Asian Initiative for Infinity Logic Summer Schools. The major topics covered set theory and recursion theory, with particular emphasis on forcing, inner model theory and Turing degrees, offering a wide overview of ideas and techniques introduced in contemporary research in the field of mathematical logic. Contents:Prikry-Type Forcings and a Forcing with Short Extenders (Moti Gitik)The Turing Degrees: An Introduction (Richard A Shore)An Introduction to Iterated Ultrapowers (John Steel) Readership: Graduate students in mathematics, and researchers in logic, set theory and computability theory. Key Features:These are notes based on short courses given by three leading experts in set theory, recursion theory and their applicationsKeywords:Logic;Set Theory;Forcing;Recursion Theory;Computability Theory;Turing Degrees;C*-algebra

Author : Damir D. Dzhafarov,Carl Mummert
Publisher : Springer Nature
Page : 498 pages
File Size : 43,6 Mb
Release : 2022-07-25
Category : Computers
ISBN : 9783031113673

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Reverse Mathematics by Damir D. Dzhafarov,Carl Mummert Pdf

Reverse mathematics studies the complexity of proving mathematical theorems and solving mathematical problems. Typical questions include: Can we prove this result without first proving that one? Can a computer solve this problem? A highly active part of mathematical logic and computability theory, the subject offers beautiful results as well as significant foundational insights. This text provides a modern treatment of reverse mathematics that combines computability theoretic reductions and proofs in formal arithmetic to measure the complexity of theorems and problems from all areas of mathematics. It includes detailed introductions to techniques from computable mathematics, Weihrauch style analysis, and other parts of computability that have become integral to research in the field. Topics and features: Provides a complete introduction to reverse mathematics, including necessary background from computability theory, second order arithmetic, forcing, induction, and model construction Offers a comprehensive treatment of the reverse mathematics of combinatorics, including Ramsey's theorem, Hindman's theorem, and many other results Provides central results and methods from the past two decades, appearing in book form for the first time and including preservation techniques and applications of probabilistic arguments Includes a large number of exercises of varying levels of difficulty, supplementing each chapter The text will be accessible to students with a standard first year course in mathematical logic. It will also be a useful reference for researchers in reverse mathematics, computability theory, proof theory, and related areas. Damir D. Dzhafarov is an Associate Professor of Mathematics at the University of Connecticut, CT, USA. Carl Mummert is a Professor of Computer and Information Technology at Marshall University, WV, USA.

Author : Richard Wentworth,Graeme Wilkin
Publisher : World Scientific
Page : 412 pages
File Size : 46,7 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 : Jordan B L Smith,Elaine Chew,Gérard Assayag
Publisher : World Scientific
Page : 316 pages
File Size : 51,8 Mb
Release : 2016-07-21
Category : Computers
ISBN : 9789813140110

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Mathemusical Conversations by Jordan B L Smith,Elaine Chew,Gérard Assayag Pdf

Mathemusical Conversations celebrates the understanding of music through mathematics, and the appreciation of mathematics through music. This volume is a compilation of the invited talks given at the Mathemusical Conversations workshop that took place in Singapore from 13–15 February 2015, organized by Elaine Chew in partnership with Gérard Assayag for the scientific program and with Bernard Lanskey for the artistic program. The contributors are world experts and leading scholars, writing on the intersection of music and mathematics. They also focus on performance and composition, two topics which are foundational both to the understanding of human creativity and to the creation of tomorrow's music technologies. This book is essential reading for researchers in both music and mathematics. It will also appeal more broadly to scholars, students, musicians, and anyone interested in new perspectives on the intimate relationship between these two universal human activities. Contents:Foreword by Series EditorsForeword by Workshop OrganizersMathemusical Engagement:Without Our Consent (Paul Schoenfield)Approaches to Musical Expression in Harmonix Video Games (Eran Egozy)Motion and Gravitation in the Musical Spheres (Elaine Chew)Mathemusical Creativity:Improvising in Creative Symbolic Interaction (Gérard Assayag)Music, Creativity, and Computers (Margaret A Boden)Tiling Canons as a Key to Approaching Open Mathematical Conjectures? (Moreno Andreatta)Shaping Performance:Musical Motives in Performance: A Study of Absolute Timing Patterns (Neta Spiro, Nicolas Gold and John Rink)Playing with Variables: Anticipating One Particular Performance of Bach's Goldberg Variations (Bernard Lanskey and Stephen Emmerson)The Informatics Philharmonic in the Indiana University Summer String Academy (Christopher Raphael)Educating the Mathemusical:Mathematical Thought and Empirical Approaches in Higher Education in Music (Jian Yang)Action and Symbol: An Essential Tension (Jeanne Bamberger)Educating the Mathemusical: Balancing the Equation (Don McLean)Geometries:Graph-theoretic and Geometric Models of Music (Richard Cohn)In Quest of Musical Vectors (Dmitri Tymoczko)A Topological Approach of Musical Relationships (Jean-Louis Giavitto and Antoine Spicher)List of Contributors Readership: Advanced secondary school students; post-secondary school students; and scientists, mathematicians, musicians and members of the public interested in the mathematical music sciences.

Author : Fei Han,Xingwang Xu,Weiping Zhang
Publisher : World Scientific
Page : 220 pages
File Size : 40,9 Mb
Release : 2016-04-18
Category : Mathematics
ISBN : 9789813100565

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Geometric Analysis Around Scalar Curvatures by Fei Han,Xingwang Xu,Weiping Zhang Pdf

This volume contains three expanded lecture notes from the program Scalar Curvature in Manifold Topology and Conformal Geometry that was held at the Institute for Mathematical Sciences from 1 November to 31 December 2014. The first chapter surveys the recent developments on the fourth-order equations with negative exponent from geometric points of view such as positive mass theorem and uniqueness results. The next chapter deals with the recent important progress on several conjectures such as the existence of non-flat smooth hyper-surfaces and Serrin's over-determined problem. And the final chapter induces a new technique to handle the equation with critical index and the sign change coefficient as well as the negative index term. These topics will be of interest to those studying conformal geometry and geometric partial differential equations. Contents:Lectures on the Fourth-Order Q Curvature Equation (Fengbo Hang and Paul C Yang)An Introduction to the Finite and Infinite Dimensional Reduction Methods (Manuel del Pino and Juncheng Wei)Einstein Constraint Equations on Riemannian Manifolds (Quôc Anh Ngô) Readership: Advanced undergraduates, graduate students and researchers interested in the study of conformal geometry and geometric partial differential equations.

Author : Ohya Masanori,Hida Takeyuki,Chen Louis Hsiao Yun
Publisher : World Scientific
Page : 244 pages
File Size : 47,8 Mb
Release : 2017-08-29
Category : Language Arts & Disciplines
ISBN : 9789813225473

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White Noise Analysis And Quantum Information by Ohya Masanori,Hida Takeyuki,Chen Louis Hsiao Yun Pdf

This volume is to pique the interest of many researchers in the fields of infinite dimensional analysis and quantum probability. These fields have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. These fields are rather wide and are of a strongly interdisciplinary nature. For such a purpose, we strove to bridge among these interdisciplinary fields in our Workshop on IDAQP and their Applications that was held at the Institute for Mathematical Sciences, National University of Singapore from 3–7 March 2014. Readers will find that this volume contains all the exciting contributions by well-known researchers in search of new directions in these fields. Contents: Extensions of Quantum Theory Canonically Associated to Classical Probability Measures (Luigi Accardi)Hida Distribution Construction of Indefinite Metric (ϕp)d (d ≥ 4) Quantum Field Theory (Sergio Albeverio and Minoru W Yoshida)A Mathematical Realization of von Neumann's Measurement Scheme (Masanari Asano, Masanori Ohya and Yuta Yamamori)On Random White Noise Processes with Memory for Time Series Analysis (Christopher C Bernido and M Victoria Carpio-Bernido)Self-Repelling (Fractional) Brownian Motion: Results and Open Questions (Jinky Bornales and Ludwig Streit)Normal Approximation for White Noise Functionals by Stein's Method and Hida Calculus (Louis H Y Chen, Yuh-Jia Lee and Hsin-Hung Shih)Sensitive Homology Searching Based on MTRAP Alignment (Toshihide Hara and Masanori Ohya)Some of the Future Directions of White Noise Theory (Takeyuki Hida)Local Statistics for Random Selfadjoint Operators (Peter D Hislop and Maddaly Krishna)Multiple Markov Properties of Gaussian Processes and Their Control (Win Win Htay)Quantum Stochastic Differential Equations Associated with Square of Annihilation and Creation Processes (Un Cig Ji and Kalyan B Sinha)Itô Formula for Generalized Real and Complex White Noise Functionals (Yuh-Jia Lee)Quasi Quantum Quadratic Operators of 𝕄2(ℂ) (Farrukh Mukhamedov)New Noise Depending on the Space Parameter and the Concept of Multiplicity (Si Si)A Hysteresis Effect on Optical Illusion and Non-Kolmogorovian Probability Theory (Masanari Asano, Andrei Khrennikov, Masanori Ohya and Yoshiharu Tanaka)Note on Entropy-Type Complexity of Communication Processes (Noboru Watanabe) Readership: Mathematicians, physicists, biologists, and information scientists as well as advanced undergraduates, and graduate students studying in these fields. All researchers interested in the study of Quantum Information and White Noise Theory. Keywords: White Noise Analysis;Quantum Information;Quantum Probability;Bioinformatics;Genes;Adaptive Dynamics;Entanglement;Quantum Entropy;Non-Kolmogorovian Probability;Infinite Dimensional AnalysisReview: Key Features: Mainly focused on quantum information theory and white noise analysis in line with the fields of infinite dimensional analysis and quantum probabilityWhite noise analysis is in a leading position of the analysis on modern stochastic analysis, and this volume contains contributions to the development of these new exciting directions

Author : Raghavan Dilip,Friedman Sy-david,Yang Yue
Publisher : World Scientific
Page : 280 pages
File Size : 55,7 Mb
Release : 2017-06-22
Category : Mathematics
ISBN : 9789813223530

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Sets And Computations by Raghavan Dilip,Friedman Sy-david,Yang Yue Pdf

The contents in this volume are based on the program Sets and Computations that was held at the Institute for Mathematical Sciences, National University of Singapore from 30 March until 30 April 2015. This special collection reports on important and recent interactions between the fields of Set Theory and Computation Theory. This includes the new research areas of computational complexity in set theory, randomness beyond the hyperarithmetic, powerful extensions of Goodstein's theorem and the capturing of large fragments of set theory via elementary-recursive structures. Further chapters are concerned with central topics within Set Theory, including cardinal characteristics, Fraïssé limits, the set-generic multiverse and the study of ideals. Also Computation Theory, which includes computable group theory and measure-theoretic aspects of Hilbert's Tenth Problem. A volume of this broad scope will appeal to a wide spectrum of researchers in mathematical logic.

Author : Andrés Eduardo Caicedo,James Cummings,Peter Koellner,Paul B. Larson
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 42,9 Mb
Release : 2017-05-12
Category : Continuum hypothesis
ISBN : 9781470422561

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Foundations of Mathematics by Andrés Eduardo Caicedo,James Cummings,Peter Koellner,Paul B. Larson Pdf

This volume contains the proceedings of the Logic at Harvard conference in honor of W. Hugh Woodin's 60th birthday, held March 27–29, 2015, at Harvard University. It presents a collection of papers related to the work of Woodin, who has been one of the leading figures in set theory since the early 1980s. The topics cover many of the areas central to Woodin's work, including large cardinals, determinacy, descriptive set theory and the continuum problem, as well as connections between set theory and Banach spaces, recursion theory, and philosophy, each reflecting a period of Woodin's career. Other topics covered are forcing axioms, inner model theory, the partition calculus, and the theory of ultrafilters. This volume should make a suitable introduction to Woodin's work and the concerns which motivate it. The papers should be of interest to graduate students and researchers in both mathematics and philosophy of mathematics, particularly in set theory, foundations and related areas.

Author : Sergey Kushnarev,Anqi Qiu,Laurent Younes
Publisher : World Scientific
Page : 220 pages
File Size : 48,7 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.

Author : Weizhu Bao,Peter A Markowich,Benoit Perthame,Eitan Tadmor
Publisher : World Scientific
Page : 243 pages
File Size : 50,9 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 : Weizhu Bao,Yongyong Cai,Ionut Danaila,Peter A Markowich
Publisher : World Scientific
Page : 361 pages
File Size : 44,9 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 : Matthias Birkner,Rongfeng Sun,Jan M. Swart
Publisher : World Scientific
Page : 363 pages
File Size : 43,5 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 : Paul-Elliot Anglès D’Auriac,Peter A. Cholak,Damir D. Dzhafarov,Benoît Monin,Ludovic Patey
Publisher : American Mathematical Society
Page : 130 pages
File Size : 46,8 Mb
Release : 2024-02-01
Category : Mathematics
ISBN : 9781470467319

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Milliken’s Tree Theorem and Its Applications: A Computability-Theoretic Perspective by Paul-Elliot Anglès D’Auriac,Peter A. Cholak,Damir D. Dzhafarov,Benoît Monin,Ludovic Patey Pdf

View the abstract.

Author : Anonim
Publisher : Unknown
Page : 1884 pages
File Size : 55,5 Mb
Release : 2005
Category : Mathematics
ISBN : UVA:X006195258

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Mathematical Reviews by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 568 pages
File Size : 46,8 Mb
Release : 1993
Category : Philosophy
ISBN : UCSC:32106020961691

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The Philosopher's Index by Anonim Pdf

Vols. for 1969- include a section of abstracts.