Notices of the International Congress of Chinese Mathematicians

Volume 5 (2017)

Number 2

Aspects on Mean Field Equations with Multiple Singular Sources on Flat Tori

Pages: 52 – 59

DOI: http://dx.doi.org/10.4310/ICCM.2017.v5.n2.a5

Author

Zhijie Chen (Department of Mathematical Sciences, Yau Mathematical Sciences Center, Tsinghua University, Beijing, China)

Abstract

This is a survey on some recent advances on the mean field equation with multiple singular sources on flat tori, mainly based on a joint project with T.-J. Kuo and C.-S. Lin. Recent theories indicate that this equation has essential relations with several different subjects, such as the complex linear ODE with the Treibich–Verdier potential, Painlevé VI equation and premodular forms. Besides reviewing the known results and announcing new results, I will also raise some open questions from these different aspects.

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Published 8 December 2017