Recent progress in mathematics / Nam-Gyu Kang, Jaigyoung Choe, Kyeongsu Choi, Sang-hyun Kim, editors.
Kang, Nam-Gyu, editor.; Choe, Jaigyoung, editor.; Choi, Kyeongsu, editor.; Kim, Sang-hyun, 1975- editor.
2022
QA564
Available Online

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Title Recent progress in mathematics / Nam-Gyu Kang, Jaigyoung Choe, Kyeongsu Choi, Sang-hyun Kim, editors.
ISBN 9789811937088 (electronic bk.)
9811937087 (electronic bk.)
9789811937071
9811937079
DOI https://doi.org/10.1007/978-981-19-3708-8
Published Singapore : Springer, 2022.
Language English
Description 1 online resource : illustrations (black and white, and color).
Other Standard Identifiers 10.1007/978-981-19-3708-8 doi
Call Number QA564
Dewey Decimal Classification 516.3/5
Summary 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, DonaldsonThomas theory for CalabiYau 4-folds, and VafaWitten invariants. Dongho Chae discusses the finite-time singularity problem for three-dimensional incompressible Euler equations. He presents Kato's classical local well-posedness results, BealeKatoMajda'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 classication of all the singularity models in a three-dimensional Riemannian manifold. He gives an alternative proof of the classication of noncollapsed steady gradient Ricci solitons in dimension 3. Hyeonbae Kang reviews some of the developments in the NeumannPoincare 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" ane algebraic varieties. .
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Added Author Kang, Nam-Gyu, editor.
Choe, Jaigyoung, editor.
Choi, Kyeongsu, editor.
Kim, Sang-hyun, 1975- editor.
Series KIAS Springer Series in Mathematics Ser.
Available in Other Form Recent progress in mathematics.
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Record Appears in Online Resources > Ebooks
All Resources
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-Poincare Operator, A Review
Danny Calegari: Sausages and Butcher Paper.

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