String Math 2022
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String Math 2022
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Author : Ron Donagi
language : en
Publisher: American Mathematical Society
Release Date : 2024-04-18
String Math 2022 written by Ron Donagi and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-18 with Mathematics categories.
This is a proceedings volume from the String-Math conference which took place at the University of Warsaw in 2022. This 12th String-Math conference focused on several research areas actively developing these days. They included generalized (categorical) symmetries in quantum field theory and their relation to topological phases of matter; formal aspects of quantum field theory, in particular twisted holography; various developments in supersymmetric gauge theories, BPS counting and Donaldson–Thomas invariants. Other topics discussed at this conference included new advances in Gromov–Witten theory, curve counting, and Calabi–Yau manifolds. Another broad topic concerned algebraic aspects of conformal field theory, vertex operator algebras, and quantum groups. Furthermore, several other recent developments were presented during the conference, such as understanding the role of operator algebras in the presence of gravity, derivation of gauge-string duality, complexity of black holes, or mathematical aspects of the amplituhedron. This proceedings volume contains articles summarizing 14 conference lectures, devoted to the above topics.
Categorical Combinatorial And Geometric Representation Theory And Related Topics
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Author : Pramod N. Achar
language : en
Publisher: American Mathematical Society
Release Date : 2024-07-11
Categorical Combinatorial And Geometric Representation Theory And Related Topics written by Pramod N. Achar and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-11 with Mathematics categories.
This book is the third Proceedings of the Southeastern Lie Theory Workshop Series covering years 2015–21. During this time five workshops on different aspects of Lie theory were held at North Carolina State University in October 2015; University of Virginia in May 2016; University of Georgia in June 2018; Louisiana State University in May 2019; and College of Charleston in October 2021. Some of the articles by experts in the field describe recent developments while others include new results in categorical, combinatorial, and geometric representation theory of algebraic groups, Lie (super) algebras, and quantum groups, as well as on some related topics. The survey articles will be beneficial to junior researchers. This book will be useful to any researcher working in Lie theory and related areas.
Frontiers In Geometry And Topology
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Author : Paul M. N. Feehan
language : en
Publisher: American Mathematical Society
Release Date : 2024-07-19
Frontiers In Geometry And Topology written by Paul M. N. Feehan and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-19 with Mathematics categories.
This volume contains the proceedings of the summer school and research conference “Frontiers in Geometry and Topology”, celebrating the sixtieth birthday of Tomasz Mrowka, which was held from August 1–12, 2022, at the Abdus Salam International Centre for Theoretical Physics (ICTP). The summer school featured ten lecturers and the research conference featured twenty-three speakers covering a range of topics. A common thread, reflecting Mrowka's own work, was the rich interplay among the fields of analysis, geometry, and topology. Articles in this volume cover topics including knot theory; the topology of three and four-dimensional manifolds; instanton, monopole, and Heegaard Floer homologies; Khovanov homology; and pseudoholomorphic curve theory.
Open Problems In Algebraic Combinatorics
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Author : Christine Berkesch
language : en
Publisher: American Mathematical Society
Release Date : 2024-08-21
Open Problems In Algebraic Combinatorics written by Christine Berkesch and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-21 with Mathematics categories.
In their preface, the editors describe algebraic combinatorics as the area of combinatorics concerned with exact, as opposed to approximate, results and which puts emphasis on interaction with other areas of mathematics, such as algebra, topology, geometry, and physics. It is a vibrant area, which saw several major developments in recent years. The goal of the 2022 conference Open Problems in Algebraic Combinatorics 2022 was to provide a forum for exchanging promising new directions and ideas. The current volume includes contributions coming from the talks at the conference, as well as a few other contributions written specifically for this volume. The articles cover the majority of topics in algebraic combinatorics with the aim of presenting recent important research results and also important open problems and conjectures encountered in this research. The editors hope that this book will facilitate the exchange of ideas in algebraic combinatorics.
The Computer Algebra System Oscar
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Author : Wolfram Decker
language : en
Publisher: Springer Nature
Release Date : 2025-01-30
The Computer Algebra System Oscar written by Wolfram Decker and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-30 with Mathematics categories.
This book presents version 1.0 of the new Computer Algebra System OSCAR. Written in Julia, OSCAR builds on and vastly extends four cornerstone systems: ANTIC for number theory, GAP for group and representation theory, polymake for polyhedral and tropical geometry, and Singular for commutative algebra and algebraic geometry. It offers powerful computational tools that transcend the boundaries of the individual disciplines involved. It is freely available, open source software. The book is an invitation to use OSCAR. With discussions of theoretical and algorithmic aspects included, it offers a multitude of explicit code snippets. These are valuable for interested researchers from graduate students through established experts.
Handbook Of Quantum Gravity
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Author : Cosimo Bambi
language : en
Publisher: Springer Nature
Release Date : 2024-12-03
Handbook Of Quantum Gravity written by Cosimo Bambi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-03 with Science categories.
The search for a theory of quantum gravity is one of the most important and fascinating problems in modern theoretical physics. While we do not have yet a complete theory of quantum gravity, significant advancements have been done in the past decades. In this handbook, every section is dedicated to a specific approach towards a theory of quantum gravity and is edited by the leading experts in the field. This book represents both a valuable resource for graduate students and an important reference for researchers in quantum gravity.
Machine Learning In Pure Mathematics And Theoretical Physics
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Author : Yang-hui He
language : en
Publisher: World Scientific
Release Date : 2023-06-21
Machine Learning In Pure Mathematics And Theoretical Physics written by Yang-hui He and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-21 with Computers categories.
The juxtaposition of 'machine learning' and 'pure mathematics and theoretical physics' may first appear as contradictory in terms. The rigours of proofs and derivations in the latter seem to reside in a different world from the randomness of data and statistics in the former. Yet, an often under-appreciated component of mathematical discovery, typically not presented in a final draft, is experimentation: both with ideas and with mathematical data. Think of the teenage Gauss, who conjectured the Prime Number Theorem by plotting the prime-counting function, many decades before complex analysis was formalized to offer a proof.Can modern technology in part mimic Gauss's intuition? The past five years saw an explosion of activity in using AI to assist the human mind in uncovering new mathematics: finding patterns, accelerating computations, and raising conjectures via the machine learning of pure, noiseless data. The aim of this book, a first of its kind, is to collect research and survey articles from experts in this emerging dialogue between theoretical mathematics and machine learning. It does not dwell on the well-known multitude of mathematical techniques in deep learning, but focuses on the reverse relationship: how machine learning helps with mathematics. Taking a panoramic approach, the topics range from combinatorics to number theory, and from geometry to quantum field theory and string theory. Aimed at PhD students as well as seasoned researchers, each self-contained chapter offers a glimpse of an exciting future of this symbiosis.
Geometric Science Of Information
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Author : Frank Nielsen
language : en
Publisher: Springer Nature
Release Date : 2023-07-31
Geometric Science Of Information written by Frank Nielsen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Computers categories.
This book constitutes the proceedings of the 6th International Conference on Geometric Science of Information, GSI 2023, held in St. Malo, France, during August 30-September 1, 2023. The 125 full papers presented in this volume were carefully reviewed and selected from 161 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: geometry and machine learning; divergences and computational information geometry; statistics, topology and shape spaces; geometry and mechanics; geometry, learning dynamics and thermodynamics; quantum information geometry; geometry and biological structures; geometry and applications.
Calabi Yau Manifolds A Bestiary For Physicists 2nd Edition
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Author : Tristan Hubsch
language : en
Publisher: World Scientific
Release Date : 2024-12-17
Calabi Yau Manifolds A Bestiary For Physicists 2nd Edition written by Tristan Hubsch and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-17 with Science categories.
Calabi-Yau spaces are complex spaces with a vanishing first Chern class, or, equivalently, with a trivial canonical bundle (sheaf), so they admit a Ricci-flat Kähler metric that satisfies the vacuum Einstein equations. Used to construct possibly realistic (super)string models, they are being studied vigorously by physicists and mathematicians alike. Calabi-Yau spaces have also turned up in computations of probability amplitudes in quantum field theory. This book collects and reviews relevant results on several major techniques of (1) constructing such spaces and (2) computing physically relevant quantities such as spectra of massless fields and their Yukawa interactions. These are amended by (3) stringy corrections and (4) results about the moduli space and its geometry, including a preliminary discussion of the still conjectural universal deformation space. It also contains a lexicon of assorted terms and important results and theorems, which can be used independently.The first edition of Calabi-Yau Manifolds: A Bestiary for Physicists was the first systematic book covering Calabi-Yau spaces, related mathematics, and their application in physics. Thirty years on, this new edition explores the intense development in the field since 1992, providing an additional 400 references. It also addresses advances in machine learning and other computer-aided methods that have recently made physically relevant computations feasible, opened new avenues in the field, and begun to deliver concretely on the now 40-year-old promise of string theory. The presentation of ideas, results, and computational methods is complemented by detailed models and sample computations throughout. This second edition also contains a new closing section, outlining the staggering advances of the past three decades and providing suggestions for future reading.
Handbook Of Geometry And Topology Of Singularities Vii
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Author : José Luis Cisneros-Molina
language : en
Publisher: Springer Nature
Release Date : 2025-03-01
Handbook Of Geometry And Topology Of Singularities Vii written by José Luis Cisneros-Molina and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-01 with Mathematics categories.
This is the seventh volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of fourteen chapters that provide an in-depth and reader-friendly introduction to various important aspects of singularity theory. The volume begins with an outstanding exposition on Jim Damon’s contributions to singularity theory and its applications. Jim passed away in 2022 and he was one of the greatest mathematicians of recent times, having made remarkable contributions to singularity theory and its applications, mostly to medical image computing. The next chapter focuses on the singularities of real functions and their bifurcation sets. Then, we look at the perturbation theory of polynomials and linear operators, complex analytic frontal singularities, the global singularity theory of differentiable maps, and the singularities of holomorphic functions from a global point of view. The volume continues with an overview of new tools in singularity theory that spring from symplectic geometry and Floer-type homology theories. Then, it looks at the derivation of Lie algebras of isolated singularities and the three-dimensional rational isolated complete intersection singularities, as well as recent developments in algebraic K-stability and the stable degeneration conjecture. This volume also contains an interesting survey on V-filtrations, a theory began by Malgrange and Kashiwara that can be used to study nearby and vanishing cycle functors and introduced by Deligne. Then, we present a panoramic view of the Hodge, toric, and motivic methods in the study of Milnor fibers in singularity theory, both from local and global points of view. The Monodromy conjecture is also explained; this is a longstanding open problem in singularity theory that lies at the crossroads of number theory, algebra, analysis, geometry, and topology. This volume closes with recent developments in the study of the algebraic complexity of optimization problems in applied algebraic geometry and algebraic statistics. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.