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The Orbit Method in Geometry and Physics
The orbit method influenced the development of several areas of mathematics in the second half of the 20th century and remains a useful and powerful tool in such areas as Lie theory, representation theory, integrable systems, complex geometry, and mathematical physics. Among the distinguished names associated with the orbit method is that of A.A. Kirillov, whose pioneering paper on nilpotent orbits (1962), places him as the founder of orbit theory. The original research papers in this volume are written by prominent mathematicians and reflect recent achievements in orbit theory and other closely related areas such as harmonic analysis, classical representation theory, Lie superalgebras, Pois...
Lie Theory and Its Applications in Physics
This volume presents modern trends in the area of symmetries and their applications based on contributions from the workshop "Lie Theory and Its Applications in Physics", held near Varna, Bulgaria, in June 2015. Traditionally, Lie theory is a tool to build mathematical models for physical systems.Recently, the trend has been towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are employed in their widest sense, embracing representation theory, algebraic geometry, number theory, infinite-dimensional ...
Highlights in Lie Algebraic Methods
This volume consists of expository and research articles that highlight the various Lie algebraic methods used in mathematical research today. Key topics discussed include spherical varieties, Littelmann Paths and Kac–Moody Lie algebras, modular representations, primitive ideals, representation theory of Artin algebras and quivers, Kac–Moody superalgebras, categories of Harish–Chandra modules, cohomological methods, and cluster algebras.
Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1
This book is the first volume of proceedings from the joint conference X International Symposium “Quantum Theory and Symmetries” (QTS-X) and XII International Workshop “Lie Theory and Its Applications in Physics” (LT-XII), held on 19–25 June 2017 in Varna, Bulgaria. The QTS series was founded on the core principle that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium at the forefront of theoretical and mathematical physics. The LT series covers the whole field of Lie theory in its widest sense, together with its applications in many areas of physics. As an interface between mathematics and physics, the workshop serves as a meeting place...
Representations and Nilpotent Orbits of Lie Algebraic Systems
This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,” the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.
Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2
This book is the second volume of the proceedings of the joint conference X. International Symposium “Quantum Theory and Symmetries” (QTS-X) and XII. International Workshop “Lie Theory and Its Applications in Physics” (LT-XII), 19–25 June 2017, Varna, Bulgaria. The QTS series started around the core concept that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium on the frontiers of theoretical and mathematical physics. The LT series covers the whole field of Lie Theory in its widest sense together with its applications in many facets of physics. As an interface between mathematics and physics the workshop serves as a meeting place for mat...
Mathematical Optimization Theory and Operations Research: Recent Trends
This book constitutes refereed proceedings of the 20th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2021, held in Irkutsk, Russia, in July 2021. Due to the COVID-19 pandemic the conference was held online. The 31 full papers and 3 short papers presented in this volume were carefully reviewed and selected from a total of 102 submissions. The papers in the volume are organised according to the following topical headings: continuous optimization; integer programming and combinatorial optimization; operational research applications; optimal control.
Topological Persistence in Geometry and Analysis
The theory of persistence modules originated in topological data analysis and became an active area of research in algebraic topology. This book provides a concise and self-contained introduction to persistence modules and focuses on their interactions with pure mathematics, bringing the reader to the cutting edge of current research. In particular, the authors present applications of persistence to symplectic topology, including the geometry of symplectomorphism groups and embedding problems. Furthermore, they discuss topological function theory, which provides new insight into oscillation of functions. The book is accessible to readers with a basic background in algebraic and differential topology.
Algebraic and Analytic Methods in Representation Theory
This book is a compilation of several works from well-recognized figures in the field of Representation Theory. The presentation of the topic is unique in offering several different points of view, which should makethe book very useful to students and experts alike.Presents several different points of view on key topics in representation theory, from internationally known experts in the field
