Geometry and Quantization of Moduli Spaces - 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 Geometry and Quantization of Moduli Spaces write by Vladimir Fock. This book was released on 2016-12-25. Geometry and Quantization of Moduli Spaces available in PDF, EPUB and Kindle. This volume is based on four advanced courses held at the Centre de Recerca Matemàtica (CRM), Barcelona. It presents both background information and recent developments on selected topics that are experiencing extraordinary growth within the broad research area of geometry and quantization of moduli spaces. The lectures focus on the geometry of moduli spaces which are mostly associated to compact Riemann surfaces, and are presented from both classical and quantum perspectives.
The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles
The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles - 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 The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles write by Richard Wentworth. This book was released on 2018-06-28. The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles available in PDF, EPUB and Kindle. 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.
Noncommutative Geometry, Quantum Fields and Motives
Noncommutative Geometry, Quantum Fields and Motives - 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 Noncommutative Geometry, Quantum Fields and Motives write by Alain Connes. This book was released on 2019-03-13. Noncommutative Geometry, Quantum Fields and Motives available in PDF, EPUB and Kindle. The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.
Lectures on Algebraic Categorification
Lectures on Algebraic Categorification - 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 Lectures on Algebraic Categorification write by Volodymyr Mazorchuk. This book was released on 2012. Lectures on Algebraic Categorification available in PDF, EPUB and Kindle. The term "categorification" was introduced by Louis Crane in 1995 and refers to the process of replacing set-theoretic notions by the corresponding category-theoretic analogues. This text mostly concentrates on algebraical aspects of the theory, presented in the historical perspective, but also contains several topological applications, in particular, an algebraic (or, more precisely, representation-theoretical) approach to categorification. It consists of fifteen sections corresponding to fifteen one-hour lectures given during a Master Class at Aarhus University, Denmark in October 2010. There are some exercises collected at the end of the text and a rather extensive list of references. Video recordings of all (but one) lectures are available from the Master Class website. The book provides an introductory overview of the subject rather than a fully detailed monograph. Emphasis is on definitions, examples and formulations of the results. Most proofs are either briefly outlined or omitted. However, complete proofs can be found by tracking references. It is assumed that the reader is familiar with the basics of category theory, representation theory, topology and Lie algebra.
Geometry, Topology and Physics
Geometry, Topology and Physics - 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 Geometry, Topology and Physics write by Boris N. Apanasov. This book was released on 2011-06-24. Geometry, Topology and Physics available in PDF, EPUB and Kindle. The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
