Geometric Representation Theory and Gauge Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Representation Theory and Gauge Theory write by Alexander Braverman. This book was released on 2019-11-22. Geometric Representation Theory and Gauge Theory available in PDF, EPUB and Kindle. This book offers a review of the vibrant areas of geometric representation theory and gauge theory, which are characterized by a merging of traditional techniques in representation theory with the use of powerful tools from algebraic geometry, and with strong inputs from physics. The notes are based on lectures delivered at the CIME school "Geometric Representation Theory and Gauge Theory" held in Cetraro, Italy, in June 2018. They comprise three contributions, due to Alexander Braverman and Michael Finkelberg, Andrei Negut, and Alexei Oblomkov, respectively. Braverman and Finkelberg’s notes review the mathematical theory of the Coulomb branch of 3D N=4 quantum gauge theories. The purpose of Negut’s notes is to study moduli spaces of sheaves on a surface, as well as Hecke correspondences between them. Oblomkov's notes concern matrix factorizations and knot homology. This book will appeal to both mathematicians and theoretical physicists and will be a source of inspiration for PhD students and researchers.
Modern Differential Geometry in Gauge Theories
Modern Differential Geometry in Gauge Theories - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Modern Differential Geometry in Gauge Theories write by Anastasios Mallios. This book was released on 2006-07-27. Modern Differential Geometry in Gauge Theories available in PDF, EPUB and Kindle. This is original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable
Instanton Counting, Quantum Geometry and Algebra
Instanton Counting, Quantum Geometry and Algebra - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Instanton Counting, Quantum Geometry and Algebra write by Taro Kimura. This book was released on 2021-07-05. Instanton Counting, Quantum Geometry and Algebra available in PDF, EPUB and Kindle. This book pedagogically describes recent developments in gauge theory, in particular four-dimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation theory, vertex operator algebras. The key concept is the instanton, which is a solution to the anti-self-dual Yang–Mills equation in four dimensions. In the first part of the book, starting with the systematic description of the instanton, how to integrate out the instanton moduli space is explained together with the equivariant localization formula. It is then illustrated that this formalism is generalized to various situations, including quiver and fractional quiver gauge theory, supergroup gauge theory. The second part of the book is devoted to the algebraic geometric description of supersymmetric gauge theory, known as the Seiberg–Witten theory, together with string/M-theory point of view. Based on its relation to integrable systems, how to quantize such a geometric structure via the Ω-deformation of gauge theory is addressed. The third part of the book focuses on the quantum algebraic structure of supersymmetric gauge theory. After introducing the free field realization of gauge theory, the underlying infinite dimensional algebraic structure is discussed with emphasis on the connection with representation theory of quiver, which leads to the notion of quiver W-algebra. It is then clarified that such a gauge theory construction of the algebra naturally gives rise to further affinization and elliptic deformation of W-algebra.
A Study in Derived Algebraic Geometry
A Study in Derived Algebraic Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Study in Derived Algebraic Geometry write by Dennis Gaitsgory. This book was released on 2019-12-31. A Study in Derived Algebraic Geometry available in PDF, EPUB and Kindle. Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in various parts of mathematics, most prominently in representation theory. This volume develops the theory of ind-coherent sheaves in the context of derived algebraic geometry. Ind-coherent sheaves are a “renormalization” of quasi-coherent sheaves and provide a natural setting for Grothendieck-Serre duality as well as geometric incarnations of numerous categories of interest in representation theory. This volume consists of three parts and an appendix. The first part is a survey of homotopical algebra in the setting of $infty$-categories and the basics of derived algebraic geometry. The second part builds the theory of ind-coherent sheaves as a functor out of the category of correspondences and studies the relationship between ind-coherent and quasi-coherent sheaves. The third part sets up the general machinery of the $mathrm{(}infty, 2mathrm{)}$-category of correspondences needed for the second part. The category of correspondences, via the theory developed in the third part, provides a general framework for Grothendieck's six-functor formalism. The appendix provides the necessary background on $mathrm{(}infty, 2mathrm{)}$-categories needed for the third part.
Representation Theory, Mathematical Physics, and Integrable Systems
Representation Theory, Mathematical Physics, and Integrable Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Representation Theory, Mathematical Physics, and Integrable Systems write by Anton Alekseev. This book was released on 2022-02-05. Representation Theory, Mathematical Physics, and Integrable Systems available in PDF, EPUB and Kindle. Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and physicists and pay tribute to his many significant and lasting achievements. Covering the latest developments at the interface of noncommutative algebra, differential and algebraic geometry, and perspectives arising from physics, this volume explores topics such as the development of new and powerful knot invariants, new perspectives on enumerative geometry and string theory, and the introduction of cluster algebra and categorification techniques into a broad range of areas. Chapters will also cover novel applications of representation theory to random matrix theory, exactly solvable models in statistical mechanics, and integrable hierarchies. The recent progress in the mathematical and physicals aspects of deformation quantization and tensor categories is also addressed. Representation Theory, Mathematical Physics, and Integrable Systems will be of interest to a wide audience of mathematicians interested in these areas and the connections between them, ranging from graduate students to junior, mid-career, and senior researchers.
