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Schubert Calculus and Its Applications in Combinatorics and Representation Theory

Guangzhou, China, November 2017

  • Conference proceedings
  • © 2020

Overview

Editors:
  1. Jianxun Hu

    1. School of Mathematics, Sun Yat-sen University, Guangzhou, China

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  2. Changzheng Li

    1. School of Mathematics, Sun Yat-sen University, Guangzhou, China

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  3. Leonardo C. Mihalcea

    1. Department of Mathematics, Virginia Tech, Blacksburg, USA

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  • Showcases the latest advances of the major topics in Schubert Calculus
  • Provides an overview of the emerging trends in Schubert Calculus
  • Includes world-leading researchers in Schubert Calculus

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 332)

Included in the following conference series:

Conference proceedings info: ICTSC 2017.

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Table of contents (12 papers)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Factorial Flagged Grothendieck Polynomials

    • Tomoo Matsumura, Shogo Sugimoto
    Pages 1-15

  3. Flag Bundles, Segre Polynomials, and Push-Forwards

    • Lionel Darondeau, Piotr Pragacz
    Pages 17-25

  4. Order of Tangency Between Manifolds

    • Wojciech Domitrz, Piotr Mormul, Piotr Pragacz
    Pages 27-42

  5. On Schubert’s Problem of Characteristics

    • Haibao Duan, Xuezhi Zhao
    Pages 43-71

  6. Asymmetric Function Theory

    • Oliver Pechenik, Dominic Searles
    Pages 73-112

  7. Minuscule Schubert Calculus and the Geometric Satake Correspondence

    • Dave Anderson, Antonio Nigro
    Pages 113-151

  8. Positive Level, Negative Level and Level Zero

    • Finn McGlade, Arun Ram, Yaping Yang
    Pages 153-194

  9. Stable Bases of the Springer Resolution and Representation Theory

    • Changjian Su, Changlong Zhong
    Pages 195-221

  10. Characteristic Classes of Orbit Stratifications, the Axiomatic Approach

    • László M. Fehér, Richárd Rimányi, Andrzej Weber
    Pages 223-249

  11. A Survey of Recent Developments on Hessenberg Varieties

    • Hiraku Abe, Tatsuya Horiguchi
    Pages 251-279

  12. Stability of Bott–Samelson Classes in Algebraic Cobordism

    • Thomas Hudson, Tomoo Matsumura, Nicolas Perrin
    Pages 281-306

  13. Residue Mirror Symmetry for Grassmannians

    • Bumsig Kim, Jeongseok Oh, Kazushi Ueda, Yutaka Yoshida
    Pages 307-365
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  1. Schubert Calculus and Its Applications in Combinatorics and Representation Theory

Keywords

About this book

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. 

Editors and Affiliations

  • School of Mathematics, Sun Yat-sen University, Guangzhou, China

    Jianxun Hu, Changzheng Li

  • Department of Mathematics, Virginia Tech, Blacksburg, USA

    Leonardo C. Mihalcea

Bibliographic Information

  • Book Title: Schubert Calculus and Its Applications in Combinatorics and Representation Theory

  • Book Subtitle: Guangzhou, China, November 2017

  • Editors: Jianxun Hu, Changzheng Li, Leonardo C. Mihalcea

  • Series Title: Springer Proceedings in Mathematics & Statistics

  • DOI: https://doi.org/10.1007/978-981-15-7451-1

  • Publisher: Springer Singapore

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Singapore Pte Ltd. 2020

  • Hardcover ISBN: 978-981-15-7450-4Published: 25 October 2020

  • Softcover ISBN: 978-981-15-7453-5Published: 26 October 2021

  • eBook ISBN: 978-981-15-7451-1Published: 24 October 2020

  • Series ISSN: 2194-1009

  • Series E-ISSN: 2194-1017

  • Edition Number: 1

  • Number of Pages: VIII, 365

  • Number of Illustrations: 86 b/w illustrations, 30 illustrations in colour

  • Topics: Global Analysis and Analysis on Manifolds, Topological Groups, Lie Groups

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