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Poincaré’s path to uniformization. (English) Zbl 1409.30037
Ji, Lizhen (ed.) et al., Uniformization, Riemann-Hilbert correspondence, Calabi-Yau manifolds and Picard-Fuchs equations. Based on the conference, Institute Mittag-Leffler, Stockholm, Sweden, July 13–18, 2015. Somerville, MA: International Press; Beijing: Higher Education Press. Adv. Lect. Math. (ALM) 42, 55-79 (2018).
From the abstract: This study features the enormous conceptual leaps by which Poincaré in 1880, via his study of Fuch’s work, established the existence of a unique (uniformization) differential equation and thereby his theory of general transcendental automorophic (Fuchsian) functions. [$$\ldots$$]. We reconcile Poincaré’s and Klein’s divergent perspectives on uniformization with the philosophical concept of the “fundamental dialectric of mathematics”, which recognizes that a mathematical advance exists historically as both a rupture and a continuity [$$\ldots$$].
For the entire collection see [Zbl 1398.14003].
##### MSC:
 30F10 Compact Riemann surfaces and uniformization 01A55 History of mathematics in the 19th century
##### Keywords:
Riemann surfaces; uniformization; automorphic functions