Recent Progress in Mathematics: KIAS Springer Series in Mathematics, cartea 1
Editat de Nam-Gyu Kang, Jaigyoung Choe, Kyeongsu Choi, Sang-hyun Kimen Limba Engleză Paperback – 2 oct 2023
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 classicallocal 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.
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Specificații
ISBN-13: 9789811937101
ISBN-10: 9811937109
Ilustrații: VII, 200 p. 22 illus., 16 illus. in color.
Dimensiuni: 155 x 235 mm
Greutate: 0.3 kg
Ediția:1st ed. 2022
Editura: Springer Nature Singapore
Colecția Springer
Seria KIAS Springer Series in Mathematics
Locul publicării:Singapore, Singapore
ISBN-10: 9811937109
Ilustrații: VII, 200 p. 22 illus., 16 illus. in color.
Dimensiuni: 155 x 235 mm
Greutate: 0.3 kg
Ediția:1st ed. 2022
Editura: Springer Nature Singapore
Colecția Springer
Seria KIAS Springer Series in Mathematics
Locul publicării:Singapore, Singapore
Cuprins
Young-Hoon Kiem: Enumerative Geometry, before and after String Theory.- Dongho Chae: On The Singularity Problem for the Euler Equations.- Simon Brendle: Singularity Models in the Three-Dimensional Ricci Flow.- Hyeonbae Kang: Spectral Geometry and Analysis of the Neumann-Poincaré Operator, A Review.- Danny Calegari: Sausages and Butcher Paper.
Textul de pe ultima copertă
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.
Caracteristici
Includes both original research articles and surveys on the cutting edge of various fields Is written by outstanding mathematicians in each of the fields covered Provides intriguing explorations of the problems of current research and progress in mathematics