Diff. Geom, Math. Phys., PDE Seminar: Lei Zhang

  • Date: 03/07/2017
  • Time: 15:30
Lei Zhang, University of Florida

University of British Columbia


Local mass concentration and a priori estimate for singular rank 2 Toda systems


A Toda system is a nonlinear second order elliptic system with exponential nonlinearity. It is very commonly observed in physics and has many ties with algebraic geometry. From analytic viewpoints it is challenging since the solutions do not have symmetry, maximum principles cannot be applied and the structures of global solutions are incredibly complicated. In this joint work with Chang-shou Lin, Juncheng Wei and Wen Yang, we use a unified approach to discuss all rank two singular Toda systems. First for local systems we prove that all weak limits of mass concentration belong to a very small finite set. Then for systems defined on compact Riemann surface we establish some new estimates. Our approach is a combination of delicate blowup analysis and fundamental tools from algebraic geometry.

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Location: ESB 2012