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.

Inhalt
TOMOO MATSUMURA, SHOGO SUGIMOTO, FACTORIAL FLAGGED GROTHENDIECK POLYNOMIALS.- LIONEL DARONDEAU AND PIOTR PRAGACZ, FLAG BUNDLES, SEGRE POLYNOMIALS, AND PUSH-FORWARDS.- Wojciech Domitrz, Piotr Mormul and Piotr Pragacz, Order of tangency between manifolds.- Haibao Duan and Xuezhi Zhao, On Schubert's Problem of Characteristics.- OLIVER PECHENIK AND DOMINIC SEARLES, ASYMMETRIC FUNCTION THEORY.- DAVE ANDERSON AND ANTONIO NIGRO, MINUSCULE SCHUBERT CALCULUS AND THE GEOMETRIC SATAKE CORRESPONDENCE.- Finn McGlade, Arun Ram, Yaping Yang, Positive level, negative level and level zero.- CHANGJIAN SU AND CHANGLONG ZHONG, STABLE BASES OF THE SPRINGER RESOLUTION AND REPRESENTATION THEORY.- LASZLO M. FEHER, RICHARD RIMANYI, AND ANDRZEJ WEBER, CHARACTERISTIC CLASSES OF ORBIT STRATIFICATIONS, THE AXIOMATIC APPROACH.- HIRAKU ABE AND TATSUYA HORIGUCHI.- A SURVEY OF RECENT DEVELOPMENTS ON HESSENBERG VARIETIES.- THOMAS HUDSON, TOMOO MATSUMURA AND NICOLAS PERRIN, STABILITY OF BOTTSAMELSON CLASSES IN ALGEBRAIC COBORDISM.- BUMSIG KIM, JEONGSEOK OH, KAZUSHI UEDA, AND YUTAKA YOSHIDA, RESIDUE MIRROR SYMMETRY FOR GRASSMANNIANS