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Author: Jianxun Hu
Publisher: Springer Nature
ISBN: 9811574510
Category : Mathematics
Languages : en
Pages : 367
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Book Description
This book gathers research papers and surveys on the latest advances in Schubert Calculus, presented at the International Festival in Schubert Calculus, held in Guangzhou, China on November 6–10, 2017. With roots in enumerative geometry and Hilbert's 15th problem, modern Schubert Calculus studies classical and quantum intersection rings on spaces with symmetries, such as flag manifolds. The presence of symmetries leads to particularly rich structures, and it connects Schubert Calculus to many branches of mathematics, including algebraic geometry, combinatorics, representation theory, and theoretical physics. For instance, the study of the quantum cohomology ring of a Grassmann manifold combines all these areas in an organic way. The book is useful for researchers and graduate students interested in Schubert Calculus, and more generally in the study of flag manifolds in relation to algebraic geometry, combinatorics, representation theory and mathematical physics.
Author: Jianxun Hu
Publisher: Springer Nature
ISBN: 9811574510
Category : Mathematics
Languages : en
Pages : 367
Get Book Here
Book Description
This book gathers research papers and surveys on the latest advances in Schubert Calculus, presented at the International Festival in Schubert Calculus, held in Guangzhou, China on November 6–10, 2017. With roots in enumerative geometry and Hilbert's 15th problem, modern Schubert Calculus studies classical and quantum intersection rings on spaces with symmetries, such as flag manifolds. The presence of symmetries leads to particularly rich structures, and it connects Schubert Calculus to many branches of mathematics, including algebraic geometry, combinatorics, representation theory, and theoretical physics. For instance, the study of the quantum cohomology ring of a Grassmann manifold combines all these areas in an organic way. The book is useful for researchers and graduate students interested in Schubert Calculus, and more generally in the study of flag manifolds in relation to algebraic geometry, combinatorics, representation theory and mathematical physics.
Author: Thomas Lam
Publisher: Springer
ISBN: 1493906828
Category : Mathematics
Languages : en
Pages : 226
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Book Description
This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the current open problems. Affine Schubert calculus lies at the crossroads of combinatorics, geometry, and representation theory. Its modern development is motivated by two seemingly unrelated directions. One is the introduction of k-Schur functions in the study of Macdonald polynomial positivity, a mostly combinatorial branch of symmetric function theory. The other direction is the study of the Schubert bases of the (co)homology of the affine Grassmannian, an algebro-topological formulation of a problem in enumerative geometry. This is the first introductory text on this subject. It contains many examples in Sage, a free open source general purpose mathematical software system, to entice the reader to investigate the open problems. This book is written for advanced undergraduate and graduate students, as well as researchers, who want to become familiar with this fascinating new field.
Author:
Publisher: Academic Press
ISBN: 0080874207
Category : Mathematics
Languages : en
Pages : 385
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Book Description
Vector Bundles - Vol 1
Author: Kevin Purbhoo
Publisher: Ann Arbor, Mich. : University Microfilms International
ISBN:
Category :
Languages : en
Pages : 218
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Book Description
Author: Martin Schubert
Publisher: Springer Science & Business Media
ISBN: 3642246214
Category : Technology & Engineering
Languages : en
Pages : 246
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Book Description
This book develops a mathematical framework for modeling and optimizing interference-coupled multiuser systems. At the core of this framework is the concept of general interference functions, which provides a simple means of characterizing interdependencies between users. The entire analysis builds on the two core axioms scale-invariance and monotonicity. The proposed network calculus has its roots in power control theory and wireless communications. It adds theoretical tools for analyzing the typical behavior of interference-coupled networks. In this way it complements existing game-theoretic approaches. The framework should also be viewed in conjunction with optimization theory. There is a fruitful interplay between the theory of interference functions and convex optimization theory. By jointly exploiting the properties of interference functions, it is possible to design algorithms that outperform general-purpose techniques that only exploit convexity. The title “network calculus” refers to the fact that the theory of interference functions constitutes a generic theoretical framework for the analysis of interference coupled systems. Certain operations within the framework are “closed”, that is, combinations of interference functions are interference functions again. Also, certain properties are preserved under such operations. This, provides a methodology for analyzing different multiuser performance measures that can be expressed as interference functions or combinations of interference functions.
Author: Ezra Miller
Publisher: Springer Science & Business Media
ISBN: 9780387237077
Category : Mathematics
Languages : en
Pages : 442
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Book Description
Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs
Author: Thomas Lam
Publisher:
ISBN: 9781493906833
Category :
Languages : en
Pages : 228
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Book Description
Author: Letterio Gatto
Publisher:
ISBN: 9788524402272
Category :
Languages : en
Pages : 121
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Book Description
Author: William Fulton
Publisher: Lecture Notes in Mathematics
ISBN:
Category : Mathematics
Languages : en
Pages : 168
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Book Description
Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks. These notes, from a summer school in Thurnau, aim to give an introduction to these topics, and to describe recent progress on these problems. There are interesting interactions with the algebra of symmetric functions and combinatorics, as well as the geometry of flag manifolds and intersection theory and algebraic geometry.
Author:
Publisher: World Scientific
ISBN:
Category :
Languages : en
Pages : 1191
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Book Description
