Schubert Calculus and Its Applications in Combinatorics and Representation 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 Schubert Calculus and Its Applications in Combinatorics and Representation Theory write by Jianxun Hu. This book was released on 2020-10-24. Schubert Calculus and Its Applications in Combinatorics and Representation Theory available in PDF, EPUB and Kindle. 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.
k-Schur Functions and Affine Schubert Calculus
k-Schur Functions and Affine Schubert Calculus - 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 k-Schur Functions and Affine Schubert Calculus write by Thomas Lam. This book was released on 2014-06-05. k-Schur Functions and Affine Schubert Calculus available in PDF, EPUB and Kindle. 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.
Vector Bundles - Vol 1
Vector Bundles - Vol 1 - 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 Vector Bundles - Vol 1 write by . This book was released on 1983-02-18. Vector Bundles - Vol 1 available in PDF, EPUB and Kindle. Vector Bundles - Vol 1
Schubert Varieties and Degeneracy Loci
Schubert Varieties and Degeneracy Loci - 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 Schubert Varieties and Degeneracy Loci write by William Fulton. This book was released on 2006-11-13. Schubert Varieties and Degeneracy Loci available in PDF, EPUB and Kindle. 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.
Combinatorial Commutative Algebra
Combinatorial Commutative 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 Combinatorial Commutative Algebra write by Ezra Miller. This book was released on 2005-06-21. Combinatorial Commutative Algebra available in PDF, EPUB and Kindle. Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs
