The Mathematics Shelf.
Surveys in Differential Geometry: Volume 14
Lizhen Ji, et al.
International Press of Boston
PO Box 43502, Sommerville, MA 02143
9781571461407, $85.00, www.amazon.com
Deftly compiled and edited by the academic editorial team of Lizhen Ji (University of Michigan), Scott A. Wolpert (University of Maryland), and Shing-Tung Yau (Harvard University), "Surveys in Differential Geometry: Volume 14, Geometry of Riemann surfaces and their moduli spaces" is a collection of lectures delivered at the 2009 JDG conference. Comprising this 418-page compendium are Divisors in the moduli spaces of curves (Enrico Arbarello and Maurizio Cornalba); Stability phenomena in the topology of moduli spaces (Ralph L. Cohen); Birational aspects of the geometry of Mg(Gavril Farkas); The universal Whitham hierarchy and the geometry of the moduli space of pointed Riemann surfaces (Samuel Grushevsky and Igor Krichever); Brill-Noether theory (Joe Harris); GL+2(R)-orbit closures via topological splittings (Pascal Hubert, Erwan Lanneau, and Martin Moller); Harmonic mappings and moduli spaces of Riemann surfaces (Jurgen Jost and Shing Tung Yau); Algebraic structures on the topology of moduli spaces of curves and maps (Y.-P. Lee and R. Vakil); Recent development on the geometry of the Teichmuller and moduli spaces of Riemann surfaces (Kefeng Liu, Xiaofeng Sun, and Shing-Tung Yau); The universal properties of Teichmuller spaces (Vladimir Markovic and Dragomir Saric); Geometry of Teichmuller space with the Teichmuller metric (Howard Masur); GIT constructions of moduli spaces of stable curves and maps (Ian Morrison); Riemann surfaces, integrable hierarchies, and singularity theory (Yongbin Ruan). "Surveys in Differential Geometry: Volume 14, Geometry of Riemann surfaces and their moduli spaces" is an invaluable core addition to academic library Advanced Mathematics resource and reference collections and supplemental study lists in the specific field of Riemann Geometry.
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|Title Annotation:||Surveys in Differential Geometry: Volume 14, Geometry of Riemann|
|Article Type:||Book review|
|Date:||Jun 1, 2010|
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