Recent Progress in Mathematics
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- Hardcover ausgewählt
- Taschenbuch
- eBook
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Sprache:Englisch
48,99 €
inkl. gesetzl. MwSt.,
Beschreibung
Produktdetails
Einband
Gebundene Ausgabe
Erscheinungsdatum
01.10.2022
Abbildungen
VII, 200 p. 22 illus., 16 illus. in color.
Herausgeber
Nam-Gyu Kang + weitereVerlag
Springer SingaporeSeitenzahl
200
Maße (L/B/H)
24,1/16/1,7 cm
Gewicht
483 g
Auflage
22001 Auflage 1st edition 2022
Sprache
Englisch
ISBN
978-981-19-3707-1
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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