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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis
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Recent Progress in Mathematics (Hardcover, 1st ed. 2022)
Loot Price: R1,527
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Recent Progress in Mathematics (Hardcover, 1st ed. 2022)
Series: KIAS Springer Series in Mathematics, 1
Expected to ship within 10 - 15 working days
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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.
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