Schubert Calculus and Its Applications in Combinatorics and Representation Theory

Guangzhou, China, November 2017

Jianxun Hu, Changzheng Li, Leonardo C. Mihalcea (Herausgeber)

Buch | Softcover

365 Seiten

2021 | 1st ed. 2020
Springer Verlag, Singapore
978-981-15-7453-5 (ISBN)

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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.

T. Matsumura, S. Sugimoto, Factorial Flagged Grothendieck Polynomials.- L. Darondeau and P. Pragacz, Flag Bundles, Segre Polynomials, and Push-Forwards.- W. Domitrz, P. Mormul and P. Pragacz, Order of tangency between manifolds.- H. Duan and X. Zhao, On Schubert’s Problem of Characteristics.- O. Pechenik and D. Searles, Asymmetric Function Theory.- D. Anderson and A. Nigro, Minuscule Schubert Calculus and the Geometric Satake Correspondence.- F. McGlade, A. Ram and Y. Yang, Positive level, negative level and level zero.- C. su and C. Zhong, Stable Bases of the Springer Resolution and Representation Theory.- L. M. Fehér, R. Rimányi and A. Weber, Characteristic Classes of Orbit Stratifications, the Axiomatic Approach.- H. Abe and T. Horiguchi, A Survey of Recent Developments on Hessenberg Varieties.- T. Hudson, T. Matsumura and N. Perrin, Stability of Bott–Samelson Classes in Algebraic Cobordism.- B. Kim, J. Oh, K. Ueda, and Y. Yoshida, ResidueMirror Symmetry for Grassmannians.

Erscheinungsdatum	29.10.2021
Reihe/Serie	Springer Proceedings in Mathematics & Statistics ; 332
Zusatzinfo	30 Illustrations, color; 86 Illustrations, black and white; VIII, 365 p. 116 illus., 30 illus. in color.
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	classical problems • flag manifolds • Grassmannians • Schubert calculus • Schubert varieties
ISBN-10	981-15-7453-7 / 9811574537
ISBN-13	978-981-15-7453-5 / 9789811574535
Zustand	Neuware