Recent Progress in Mathematics: 1 (KIAS Springer Series in Mathematics) - Tapa blanda

 
9789811937101: Recent Progress in Mathematics: 1 (KIAS Springer Series in Mathematics)
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ISBN 10: 9811937109 ISBN 13: 9789811937101
Editorial: Springer, 2023

Sinopsis

This book consists of five chapters presenting problems of current research in mathematics, with its history and development, current state, and possible future direction. Four of the chapters are expository in nature while one is based more directly on research. All deal with important areas of mathematics, however, such as algebraic geometry, topology, partial differential equations, Riemannian geometry, and harmonic analysis. This book is addressed to researchers who are interested in those subject areas. 

Young-Hoon Kiem discusses classical enumerative geometry before string theory and improvements after string theory as well as some recent advances in quantum singularity theory, Donaldson-Thomas theory for Calabi-Yau 4-folds, and Vafa-Witten invariants. 

Dongho Chae discusses the finite-time singularity problem for three-dimensional incompressible Euler equations. He presents Kato's classical local well-posedness results, Beale-Kato-Majda's blow-up criterion, and recent studies on the singularity problem for the 2D Boussinesq equations. 

Simon Brendle discusses recent developments that have led to a complete classification of all the singularity models in a three-dimensional Riemannian manifold. He gives an alternative proof of the classification of noncollapsed steady gradient Ricci solitons in dimension 3. 

Hyeonbae Kang reviews some of the developments in the Neumann-Poincare operator (NPO). His topics include visibility and invisibility via polarization tensors, the decay rate of eigenvalues and surface localization of plasmon, singular geometry and the essential spectrum, analysis of stress, and the structure of the elastic NPO.

Danny Calegari provides an explicit description of the shift locus as a complex of spaces over a contractible building. He describes the pieces in terms of dynamically extended laminations and of certain explicit "discriminant-like" affine algebraic varieties. 

"Sinopsis" puede pertenecer a otra edición de este libro.

De la contraportada

This book consists of five chapters presenting problems of current research in mathematics, with its history and development, current state, and possible future direction. Four of the chapters are expository in nature while one is based more directly on research. All deal with important areas of mathematics, however, such as algebraic geometry, topology, partial differential equations, Riemannian geometry, and harmonic analysis. This book is addressed to researchers who are interested in those subject areas.


Young-Hoon Kiem discusses classical enumerative geometry before string theory and improvements after string theory as well as some recent advances in quantum singularity theory, Donaldson–Thomas theory for Calabi–Yau 4-folds, and Vafa–Witten invariants. 

Dongho Chae discusses the finite-time singularity problem for three-dimensional incompressible Euler equations. He presents Kato's classical local well-posedness results, Beale–Kato–Majda's blow-up criterion, and recent studies on the singularity problem for the 2D Boussinesq equations. 

Simon Brendle discusses recent developments that have led to a complete classi?cation of all the singularity models in a three-dimensional Riemannian manifold. He gives an alternative proof of the classi?cation of noncollapsed steady gradient Ricci solitons in dimension 3. 

Hyeonbae Kang reviews some of the developments in the Neumann–Poincare operator (NPO). His topics include visibility and invisibility via polarization tensors, the decay rate of eigenvalues and surface localization of plasmon, singular geometry and the essential spectrum, analysis of stress, and the structure of the elastic NPO.

Danny Calegari provides an explicit description of the shift locus as a complex of spaces over a contractible building. He describes the pieces in terms of dynamically extended laminations and of certain explicit “discriminant-like” a?ne algebraic varieties. 

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer
Año de publicación
2023
Idioma
Inglés
ISBN 10 
9811937109
ISBN 13 
9789811937101
Encuadernación
Tapa blanda
Número de edición
1
Número de páginas
208
Editor
Kang Nam-Gyu, Choe Jaigyoung, Choi Kyeongsu, Kim Sang-hyun
Contacto del fabricante
no disponible
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ProductSafety@springernature.com
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Otras ediciones populares con el mismo título

9789811937071: Recent Progress in Mathematics: 1 (KIAS Springer Series in Mathematics, 1)

Edición Destacada

ISBN 10:  9811937079 ISBN 13:  9789811937071
Editorial: Springer, 2022
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