Softcover ISBN: 978-1-4704-7240-5
Proceedings of Symposia in Pure Mathematics Volume: 107
2024; 296 pp
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.
Graduate students and researchers interested in mathematical aspects of quantum field theory and string theory.
Articles
Hulya Arguz ? Quiver DT invariants and log Gromov?Witten theory of toric varieties
Martin Bies ? Root bundles: Applications to F-theory Standard Models
Pierrick Bousseau ? Holomorphic Floer theory and Donaldson-Thomas invariants
Kasia Budzik ? Giant Gravitons and non-conformal vacua in twisted holography
Daniel S. Freed ? Introduction to topological symmetry in QFT
Mateo Galdeano ? Superconformal algebras for the Schoen Calabi?Yau manifold
David Jordan ? Langlands duality for skein modules of 3-manifolds
Elise LePage ? Link homology from homological mirror symmetry
Nikita Nekrasov ? Analytic continuation and supersymmetry
Michele Del Zotto, Muyang Liu and Paul-Konstantin Oehlmann ? 6D heterotic little string theories and F-theory geometry: An introduction
Meng-Chwan Tan ? Vafa-Witten theory: Invariants, Floer homologies, Higgs bundles, a geometric Langlands correspondence, and categorification
Brian Williams ? A holomorphic approach to fivebranes
Edward Witten ? Algebras, regions, and observers
Mayuko Yamashita ? Invertible QFTs and differential Anderson duals
Softcover ISBN: 978-1-4704-7239-9
Contemporary Mathematics Volume: 801
2024; 260 pp
This volume contains the proceedings of the conference Recent Advances and New Directions in the Interplay of Noncommutative Algebra and Geometry, held from June 20?24, 2022, at the University of Washington, Seattle, in honor of S. Paul Smith's 65th birthday.
The articles reflect the wide interests of Smith and provide researchers and graduate students with an indispensable overview of topics of current interest. Specific fields covered include: noncommutative algebraic geometry, representation theory, Hopf algebras and quantum groups, the elliptic algebras of Feigin and Odesskii, Calabi-Yau algebras, Artin-Schelter regular algebras, deformation theory, and Lie theory.
In addition to original research contributions the volume includes an introductory essay reviewing Smith's research contributions in these fields, and several survey articles.
Graduate students and research mathematicians interested in noncommutative algebra and noncommutative algebraic geometry.
Articles
Jason P. Bell, Leon Burkhardt and Nicholas Priebe ? Ore extensions of commutative rings and the Dixmier-Moeglin equivalence
Raf Bocklandt and Jasper van de Kreeke ? Deformations of gentle A
-algebras
K. A. Brown and J. T. Stafford ? The prime spectrum of the Drinfeld double of the Jordan plane
Alex Chirvasitu, Ryo Kanda and S. Paul Smith ? Modular properties of elliptic algebras
K. R. Goodearl ? Spectra of quantum algebras
Timothy J. Hodges ? Introduction to Belavin-Drinfeld Quantum Groups
Hongdi Huang, Xin Tang and Xingting Wang ? A survey on Zariski cancellation problems for noncommutative and Poisson algebras
Colin Ingalls and Takehiko Yasuda ? Log centres of noncommutative crepant resolutions are Kawamata log terminal: Remarks on a paper of Stafford and Van den Bergh
Ian M. Musson ? On the geometry of some algebras related to the Weyl groupoid.
Pablo S. Ocal, Kenta Ueyama and Padmini Veerapen ? A primer on twists in the noncommutative realm focusing on algebra, representation theory, and geometry
Daniel Rogalski ? Artin-Schelter regular algebras
Hung V. Tran and Michaela Vancliff ? Twisting systems and some quantum P3
s with point scheme a rank-2 quadric
Michaela Vancliff ? An example of a quadratic AS-regular algebra without any point modules
Hardcover ISBN: 978-1-4704-7695-3
Graduate Studies in Mathematics Volume: 244
2024; 361 pp
Complex manifolds are smooth manifolds endowed with coordinate charts that overlap holomorphically. They have deep and beautiful applications in many areas of mathematics. This book is an introduction to the concepts, techniques, and main results about complex manifolds (mainly compact ones), and it tells a story. Starting from familiarity with smooth manifolds and Riemannian geometry, it gradually explains what is different about complex manifolds and develops most of the main tools for working with them, using the Kodaira embedding theorem as a motivating project throughout.
The approach and style will be familiar to readers of the author's previous graduate texts: new concepts are introduced gently, with as much intuition and motivation as possible, always relating new concepts to familiar old ones, with plenty of examples. The main prerequisite is familiarity with the basic results on topological, smooth, and Riemannian manifolds. The book is intended for graduate students and researchers in differential geometry, but it will also be appreciated by students of algebraic geometry who wish to understand the motivations, analogies, and analytic results that come from the world of differential geometry.
Graduate students and researchers interested in complex manifolds and differential geometry.
Chapters
The basics
Complex submanifolds
Holomorphic vector bundles
The Dolbeault complex
Sheaves
Sheaf cohomology
Connections
Hermitian and Kahler manifolds
Hodge theory
The Kodaira embedding theorem
Paperback ISBN: 9780443185052
Expected release date: August 1, 2024
Recent Trends in Fractional Calculus and Its Applications addresses the answer to this very basic question: "Why is Fractional Calculus important?" Until recent times, Fractional Calculus was considered as a rather esoteric mathematical theory without applications, but in the last few decades there has been an explosion of research activities on the application of Fractional Calculus to very diverse scientific fields ranging from the physics of diffusion and advection phenomena, to control systems to finance and economics. An important part of mathematical modelling of objects and processes is a description of their dynamics.
The term Fractional Calculus is more than 300 years old. It is a generalization of the ordinary differentiation and integration to noninteger (arbitrary) order. The subject is as old as the calculus of differentiation and goes back to times when Leibniz, Gauss, and Newton invented this kind of calculation. Several mathematicians contributed to this subject over the years. People like Liouville, Riemann, and Weyl made major contributions to the theory of Fractional Calculus. In recent decades the field of Fractional Calculus has attracted the interest of researchers in several areas, including mathematics, physics, chemistry, engineering, finance, and social sciences.
1. New Directions in Fractional Differential Equations
2. On Riesz Derivative Problems
3. Some Proposals for a Renewal in the Field of Fractional Behaviour Studies
4. The Origin of the Generalized Memory: Analysis of the Balance Equations and Corrections to Newtonfs 3rd Law
5. Modeling COVID-19 Pandemic Outbreak Using Fractional-Order Systems
6. Damage and Fatigue Described by a Fractional Model
7. Wavelet Fractional Operators
8. Fractional Calculus Applied to Image Processing
9. Dynamics, Simulation and Parameter Estimation of a Fractional Incommensurate Model Predicting Covid-19
10. Fractional Calculus and Its Applications to Biology
11. Fractional Differential Equations and its Applications in Circuits Theory
12. Fractional Calculus: A Reliable Tool for Solving Real World Problems
13. Approximation of Mild Solutions of a Semilinear Fractional Differential Equation
14. Extended Fractional Calculus
15. Fractional Calculi on Time Scales
Handbook of Statistics, Volume 51
September 1, 2024
Hardback ISBN: 9780443293283
Probability Models, Volume 51 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on Steinfs methods, Probabilities and thermodynamics third law, Random Matrix Theory, General tools for understanding fluctuations of random variables, An approximation scheme to compute the Fisher-Rao distance between multivariate normal distributions, Probability Models Applied to Reliability and Availability Engineering, Backward stochastic differential equation? Stochastic optimization theory and viscous solution of HJB equation, and much more.
Additional chapters cover Probability Models in Machine Learning, The recursive stochastic algorithm, randomized urn models and response-adaptive randomization in clinical trials, Random matrix theory: local laws and applications, KOO methods and their high-dimensional consistencies in some multivariate models, Fourteen Lectures on Inference for Stochastic Processes, and A multivariate cumulative damage model and some applications.
Preface
Arni S.R. Srinivasa Rao, Zhidong Bai and C.R. Rao
1. Steinfs methods : Qi-Man Shao and Zhuosong Zhang
2. Probabilities and thermodynamics third law : Angelo Plastino
3. Random Matrix Theory : Jeff Yao
4. General tools for understanding fluctuations of random variables : Sourav Chatterjee
5. An approximation scheme to compute the Fisher-Rao distance between multivariate normal distributions : Frank Nielsen
6. Chapter title to be confirmed : Qihua Wang
7. Probability Models Applied to Reliability and Availability Engineering : Kishor Trivedi, Kishor Trivedi and Liudong Xing
8. Backward stochastic differential equation? Stochastic optimization theory and viscous solution of HJB equation :Shige Peng
9. Probability Models in Machine Learning : Qi Meng
10. Chapter title to be confirmed : Grzegorz A. Rempala
11. The recursive stochastic algorithm, randomized urn models and response-adaptive randomization in clinical trials : Lixin Zhang
12. Random matrix theory: local laws and applications : Fan Yang, Yukun He and Zhigang Bao
13. KOO methods and their high-dimensional consistencies in some multivariate models : Y. Fujikoshi
14. Fourteen Lectures on Inference for Stochastic Processes : B.L.S. PRAKASA RAO
15. A multivariate cumulative damage model and some applications : Raul Fierro