By Filippo Bracci,Jisoo Byun,Hervé Gaussier,Kengo Hirachi,Kang-Tae Kim,Nikolay Shcherbina

This quantity comprises 28 chapters through authors who're top researchers of the realm describing some of the updated elements within the box of numerous complicated variables (SCV). those contributions are established upon their shows on the tenth Korean convention on numerous complicated Variables (KSCV10), held as a satellite tv for pc convention to the foreign Congress of Mathematicians (ICM) 2014 in Seoul, Korea.

SCV has been the time period for multidimensional complicated research, one of many relevant study components in arithmetic. experiences over the years have printed quite a few wealthy, interesting, new wisdom in advanced research and geometry of analytic areas and holomorphic capabilities that have been "hidden" on the subject of advanced measurement one. those new theories have major intersections with algebraic geometry, differential geometry, partial differential equations, dynamics, practical research and operator idea, and sheaves and cohomology, in addition to the conventional research of holomorphic capabilities in all dimensions.

This publication is appropriate for a wide viewers of mathematicians at and above the start graduate-student point. Many chapters pose open-ended difficulties for additional learn, and one particularly is dedicated to difficulties for destiny investigations.

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