Jun-Cheng Wei | PIMS - Pacific Institute for the Mathematical Sciences

Professor of Mathematics, University of British Columbia

Prof. Wei received his PhD from University of Minnesota in 1994. He was a postdoctoral fellow at SISSA (Trieste, Italy) from 1994 to 1995. In 1995 he joined the department of mathematics at Chinese University of Hong Kong where he held the Wei Lun Chair Professor from 2011 to 2013. He then moved to University of British Columbia in 2013 as a CRC in Nonlinear Partial Differential Equation. He has published extensively and his research covers both pure and applied mathematics, ranging from De Giorgi and Liouville type properties of nonlinear partial differential equations, concentration phenomena, nonlinear analysis, geometric scalar curvature problems, to reaction-diffusion systems, diblock and triblock copolymer problems, phase-transitions in material sciences and pattern formation in mathematical biology. He is an Invited Speaker at the International Congress of Mathematicians, Korea, 2014, a plenary speaker at the International Congress of Chinese Mathematicians, Beijing, 2010, and a Senior Croucher Fellow in 2005.

Dr Wei was a member of the PIMS SRP from 2015 till 2019

Abstract: I will describe some mathematical issues related to the analysis of localized patterns (spikes and interfaces) in reaction diffusion systems. For spikes, the analysis of the spectrum of various classes of nonlocal eigenvalue problems (NLEP)...

We consider fractional minimal surfaces introduced by Caffarelli, Roquejoffre and Savin (2009). Up to now the only examples of fractional minimal surfaces are hyperplanes. In this talk, we first prove the existence of the analog of fractional Lawson...

I will consider the following classical harmonic map flow from a general two-dimensional domain D to S^2: u_t=\Delta u +|\nabla u|^2 u, u: D \to S^2We develop a parabolic gluing method to construct finite time blow-up solutions of Type II in general...

Classifying solutions is one of central themes in nonlinear partial differential equations. This is the content of various Liouville type theorems and more recently De Giorgi type conjectures. I will report recent progress towards De Giorgi's...

I will report recent progress in De Giorgi's type conjectures (and beyond) for Allen-Cahn equation and some free boundary problems in the whole space.

I will discuss recent new developments in De Giorgi Conjecture for Allen-Cahn equation. In dimensions up to 10, we shall establish the C2,α estimates of level sets for stable solutions of Allen-Cahn. By applying reverse gluing method we show that the...