Uniformization, Riemann-Hilbert correspondence, Calabi-Yau manifolds & Picard-Fuchs equations / edited by Lizhen Ji, Shing-Tung Yau.

Somerville, MA : International Press, Higher Education Press [2018] , ©2018
Conference Name:
Uniformization, Riemann-Hilbert correspondence, Calabi-Yau manifolds and Picard-Fuchs equations (Conference) (2015 : Institut Mittag-Leffler)
Advanced lectures in mathematics (International Press) ; v. 42.
Advanced lectures in Mathematics ; Volume 42
ii, ii, 619 pages: illustrations ; 26 cm.
Riemann surfaces.
Curves, Algebraic.
Calabi-Yau manifolds.
Riemann surfaces.
Riemann-Hilbert problems.
Calabi-Yau manifolds.
Conference papers and proceedings.
"The uniformization theorem of Riemann surfaces is one of the most beautiful and important theorems in mathematics. Besides giving a clean classification of Riemann surfaces, its proof has motivated many new methods, such as the Riemann-Hilbert correspondence, Picard-Fuchs equations, and higher-dimensional generalizations of the uniformization theorem, which include Calabi-Yau manifolds. This volume consists of expository papers on the four topics in its title, written by experts from around the world, and is the first to put forth a comprehensive discussion of these topics, and of the relations between them"-- Page 4 of cover.
Hypergeometric functions, from Riemann till present / Frits Beukers
Picard-Fuchs uniformization of modular subvarieties / Brent Doran, Charles F. Doran, and Andrew Harder
Poincaré’s path to uniformization / Connemara Doran
Exploring modular forms and the cohomology of local systems on moduli spaces by counting points / Gerard van der Geer
Moduli spaces of compact Riemann surfaces: their complex structures and an overview of major results / Lizhen Ji
The Morrison-Kawamata cone conjecture and abundance on Ricci flat manifolds / Vladimir Lazić, Keiji Oguiso, and Thomas Peternell
Conformal geometry and the Painlevé VI Equation / Chang-Shou Lin
Calabi-Yau metrics: mirror symmetry, Hitchin systems and instanton corrections / Wenxuan Lu
Quasiconformal mappings, from Ptolemy’s geography to the work of Teichmüller / Athanase Papadopoulos
Riemann-Hilbert correspondence, irregular singularities and Hodge theory / Claude Sabbah
Krichever-Novikov type algebras and Wess-Zumino-Novikov-Witten models / Martin Schlichenmaier
Moduli of canonically polarized manifolds, higher order Kodaira-Spencer maps, and an analogy to Calabi-Yau manifolds / Georg Schumacher
Calabi–Yau operators / Duco van Straten
A survey on toric mirror symmetry / Hsian-Hua Tseng
Dynamical systems on analytic manifolds of quadratic differentials: Chapter I, F-Structures / William A. Veech
Aspects on Calabi–Yau moduli / Chin-Lung Wang
Degeneration of Ricci-flat Calabi-Yau manifolds and its applications / Yuguang Zhang
Mirror symmetry for plane cubics revisited / Jie Zhou.
"[...] A conference titled 'Uniformization, Riemann-Hilbert correspondence, Calabi-Yau manifolds & Picard-Fuchs equations' was held at Institute Mittag-Leffler in July 13-18, 2015. [...] Almost all papers of this book were contributed by speakers of this conference."- preface
Includes bibliographical references.
Ji, Lizhen, 1964- editor.
Yau, Shing-Tung, 1949- editor.
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