Abstract. It is well-known that for Liouville equation with singular sources

$$ \Delta u +\lambda e^u= 4\pi \sum_{j=1}^m \gamma_j \delta_{p_j} in \Omega, u=0 \ \mbox{on} \ \partial \Omega$$

all blow-ups are simple, provided that $\gamma_j $ are not integers (quantized singularities). For Liouville equation with quantized singular sources, the nonsimple blowup phenomenon has been a major difficulty for years. In this talk I will present recent work with D'Aprile and Lei Zhang in showing that all blow-ups are also simple, even in the quantized case.

Bio. Juncheng Wei is a Chinese mathematician working in the area of nonlinear partial differential equations nonlinear analysis and mathematical biology. Since 1994, he has over 470 published articles in top journals, including Annals of Mathematics, Inventiones Mathematicae, Communications on Pure and Applied Mathematics, and Duke Mathematical Journal. He is now a Professor of Mathematics and a Canada Research Chair (Tier I) at the University of British Columbia. He received a Silver Morningside Medal in 2010, and was an invited speaker at the 2014 International Congress of Mathematicians. In 2019, Juncheng Wei was elected a Fellow of the Royal Society of Canada. In 2020, he was awarded the CMS Jeffery-Williams Prize and Simons Fellow in Mathematics. Juncheng Wei's scholarly work has been cited over 18,000 times and has an h-index 68.