Mirror Symmetry Tropical Geometry And Representation Theory
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Mirror Symmetry Tropical Geometry And Representation Theory
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Author : Teresa Ludenbach
language : en
Publisher:
Release Date : 2023
Mirror Symmetry Tropical Geometry And Representation Theory written by Teresa Ludenbach and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.
Mirror Symmetry And Tropical Geometry
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Author : Ricardo Castaño-Bernard
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Mirror Symmetry And Tropical Geometry written by Ricardo Castaño-Bernard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
This volume contains contributions from the NSF-CBMS Conference on Tropical Geometry and Mirror Symmetry, which was held from December 13-17, 2008 at Kansas State University in Manhattan, Kansas. --
Tropical Geometry And Mirror Symmetry
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Author : Mark Gross
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-01-20
Tropical Geometry And Mirror Symmetry written by Mark Gross and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-20 with Mathematics categories.
Tropical geometry provides an explanation for the remarkable power of mirror symmetry to connect complex and symplectic geometry. The main theme of this book is the interplay between tropical geometry and mirror symmetry, culminating in a description of the recent work of Gross and Siebert using log geometry to understand how the tropical world relates the A- and B-models in mirror symmetry. The text starts with a detailed introduction to the notions of tropical curves and manifolds, and then gives a thorough description of both sides of mirror symmetry for projective space, bringing together material which so far can only be found scattered throughout the literature. Next follows an introduction to the log geometry of Fontaine-Illusie and Kato, as needed for Nishinou and Siebert's proof of Mikhalkin's tropical curve counting formulas. This latter proof is given in the fourth chapter. The fifth chapter considers the mirror, B-model side, giving recent results of the author showing how tropical geometry can be used to evaluate the oscillatory integrals appearing. The final chapter surveys reconstruction results of the author and Siebert for ``integral tropical manifolds.'' A complete version of the argument is given in two dimensions.
Homological Mirror Symmetry And Tropical Geometry
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Author : Ricardo Castano-Bernard
language : en
Publisher: Springer
Release Date : 2014-10-07
Homological Mirror Symmetry And Tropical Geometry written by Ricardo Castano-Bernard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-07 with Mathematics categories.
The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the “tropical” approach to Gromov-Witten theory and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Geometry studies piecewise-linear objects which appear as “degenerations” of the corresponding algebro-geometric objects.
Algebraic Geometry Explained
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date :
Algebraic Geometry Explained written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
Embark on a captivating journey through the world of algebraic geometry with this comprehensive and accessible guide. Delve into the intricate relationship between algebra and geometry, uncovering the hidden structures that govern the behavior of geometric objects. Discover the foundations of algebraic geometry, where we lay the groundwork for understanding algebraic varieties, the central objects of study in this field. Explore the concept of schemes, a generalized notion of space that extends the familiar concept of varieties, providing a powerful framework for studying geometric objects in great generality. Unravel the mysteries of curves, the simplest and most fundamental type of algebraic variety. Investigate their properties, classifications, and applications, uncovering their significance in diverse fields such as cryptography and error-correcting codes. Explore the realm of surfaces, two-dimensional varieties with rich geometric and topological structures. Discover quadrics, ruled and developable surfaces, and embark on a journey to classify these surfaces, revealing their unique characteristics and applications in architecture and engineering. Venture into the vast landscape of higher-dimensional varieties, where we uncover the intricate interplay between geometry and topology. Investigate intersections and cohomology, unveiling the topological secrets of varieties. Delve into the concept of divisors and linear systems, gaining insights into the behavior of algebraic varieties. Witness the power of algebraic geometry as we explore its diverse applications. Discover the connections between algebraic geometry and coding theory, cryptography, physics, and number theory, showcasing the remarkable versatility of this mathematical discipline. With clear explanations, engaging examples, and insightful connections to other areas of mathematics, this book is an essential resource for students, researchers, and anyone fascinated by the beauty and power of algebraic geometry. Immerse yourself in the world of algebraic geometry and uncover the hidden elegance that lies at the intersection of algebra and geometry. If you like this book, write a review!
Representation Theory And Mathematical Physics
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Author : Jeffrey Adams
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-11-07
Representation Theory And Mathematical Physics written by Jeffrey Adams and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-07 with Mathematics categories.
This volume contains the proceedings of the conference on Representation Theory and Mathematical Physics, in honor of Gregg Zuckerman's 60th birthday, held October 24-27, 2009, at Yale University. Lie groups and their representations play a fundamental role in mathematics, in particular because of connections to geometry, topology, number theory, physics, combinatorics, and many other areas. Representation theory is one of the cornerstones of the Langlands program in number theory, dating to the 1970s. Zuckerman's work on derived functors, the translation principle, and coherent continuation lie at the heart of the modern theory of representations of Lie groups. One of the major unsolved problems in representation theory is that of the unitary dual. The fact that there is, in principle, a finite algorithm for computing the unitary dual relies heavily on Zuckerman's work. In recent years there has been a fruitful interplay between mathematics and physics, in geometric representation theory, string theory, and other areas. New developments on chiral algebras, representation theory of affine Kac-Moody algebras, and the geometric Langlands correspondence are some of the focal points of this volume. Recent developments in the geometric Langlands program point to exciting connections between certain automorphic representations and dual fibrations in geometric mirror symmetry.
A Gentle Introduction To Homological Mirror Symmetry
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Author : Raf Bocklandt
language : en
Publisher: Cambridge University Press
Release Date : 2021-08-19
A Gentle Introduction To Homological Mirror Symmetry written by Raf Bocklandt and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-19 with Mathematics categories.
Introduction to homological mirror symmetry from the point of view of representation theory, suitable for graduate students.
Representation Theory And Beyond
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Author : Jan Šťovíček
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-11-13
Representation Theory And Beyond written by Jan Šťovíček and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-13 with Education categories.
This volume contains the proceedings of the Workshop and 18th International Conference on Representations of Algebras (ICRA 2018) held from August 8–17, 2018, in Prague, Czech Republic. It presents several themes of contemporary representation theory together with some new tools, such as stable ∞ ∞-categories, stable derivators, and contramodules. In the first part, expanded lecture notes of four courses delivered at the workshop are presented, covering the representation theory of finite sets with correspondences, geometric theory of quiver Grassmannians, recent applications of contramodules to tilting theory, as well as symmetries in the representation theory over an abstract stable homotopy theory. The second part consists of six more-advanced papers based on plenary talks of the conference, presenting selected topics from contemporary representation theory: recollements and purity, maximal green sequences, cohomological Hall algebras, Hochschild cohomology of associative algebras, cohomology of local selfinjective algebras, and the higher Auslander–Reiten theory studied via homotopy theory.
Analysis Of Stochastic Partial Differential Equations
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Author : Davar Khoshnevisan
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-06-11
Analysis Of Stochastic Partial Differential Equations written by Davar Khoshnevisan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-11 with Mathematics categories.
The general area of stochastic PDEs is interesting to mathematicians because it contains an enormous number of challenging open problems. There is also a great deal of interest in this topic because it has deep applications in disciplines that range from applied mathematics, statistical mechanics, and theoretical physics, to theoretical neuroscience, theory of complex chemical reactions [including polymer science], fluid dynamics, and mathematical finance. The stochastic PDEs that are studied in this book are similar to the familiar PDE for heat in a thin rod, but with the additional restriction that the external forcing density is a two-parameter stochastic process, or what is more commonly the case, the forcing is a "random noise," also known as a "generalized random field." At several points in the lectures, there are examples that highlight the phenomenon that stochastic PDEs are not a subset of PDEs. In fact, the introduction of noise in some partial differential equations can bring about not a small perturbation, but truly fundamental changes to the system that the underlying PDE is attempting to describe. The topics covered include a brief introduction to the stochastic heat equation, structure theory for the linear stochastic heat equation, and an in-depth look at intermittency properties of the solution to semilinear stochastic heat equations. Specific topics include stochastic integrals à la Norbert Wiener, an infinite-dimensional Itô-type stochastic integral, an example of a parabolic Anderson model, and intermittency fronts. There are many possible approaches to stochastic PDEs. The selection of topics and techniques presented here are informed by the guiding example of the stochastic heat equation. A co-publication of the AMS and CBMS.
Tensors Asymptotic Geometry And Developments 2016 2018
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Author : J.M. Landsberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-07-05
Tensors Asymptotic Geometry And Developments 2016 2018 written by J.M. Landsberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-05 with Mathematics categories.
Tensors are used throughout the sciences, especially in solid state physics and quantum information theory. This book brings a geometric perspective to the use of tensors in these areas. It begins with an introduction to the geometry of tensors and provides geometric expositions of the basics of quantum information theory, Strassen's laser method for matrix multiplication, and moment maps in algebraic geometry. It also details several exciting recent developments regarding tensors in general. In particular, it discusses and explains the following material previously only available in the original research papers: (1) Shitov's 2017 refutation of longstanding conjectures of Strassen on rank additivity and Common on symmetric rank; (2) The 2017 Christandl-Vrana-Zuiddam quantum spectral points that bring together quantum information theory, the asymptotic geometry of tensors, matrix multiplication complexity, and moment polytopes in geometric invariant theory; (3) the use of representation theory in quantum information theory, including the solution of the quantum marginal problem; (4) the use of tensor network states in solid state physics, and (5) recent geometric paths towards upper bounds for the complexity of matrix multiplication. Numerous open problems appropriate for graduate students and post-docs are included throughout.