This is the proceedings of the conference "Primitive Forms and Related Subjects" held at Kavli IPMU, the University of Tokyo in February 10–14, 2014. The principal aim of the conference was to discuss the current status of rapidly developing subjects related to primitive forms. In particular, Fukaya category, Gromov–Witten and FJRW invariants, mathematical formulation of Landau–Ginzburg models, and mirror symmetry were discussed. The conference had three introductory courses by experts, and 12 lectures on more advanced topics. The present volume contains two survarticles and 11 research articles based on them. Thus the volume is recommended both to researchers who are already experts in the subjects, and also to graduate students who are interested in and want to start study the subjects.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America

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.

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. 

This is the proceedings of the conference "Primitive Forms and Related Subjects" held at Kavli IPMU, the University of Tokyo in February 10–14, 2014. The principal aim of the conference was to discuss the current status of rapidly developing subjects related to primitive forms. In particular, Fukaya category, Gromov–Witten and FJRW invariants, mathematical formulation of Landau–Ginzburg models, and mirror symmetry were discussed. The conference had three introductory courses by experts, and 12 lectures on more advanced topics. The present volume contains two survarticles and 11 research articles based on them. Thus the volume is recommended both to researchers who are already experts in the subjects, and also to graduate students who are interested in and want to start study the subjects.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America

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.

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.