
Professor TingJung Kuo will give an intensive course of 8 lectures at Waseda University as an activity of the
This part of the course will be an introduction to the Mean Field Equation, with an emphasis on analytic techniques for solving nonlinear pde. The Mean Field Equation is closely related to the Liouville equation, and the Toda equation. It appears in theoretical physics (gauge theory), differential geometry, and the theory of integrable systems. Solutions of the Mean Field Equation with singular sources (solutions with logarithmic behaviour at isolated singular points) are particularly interesting and important, and require special techniques. The lectures will explain these techniques, starting from the simplest cases, and leading to nontrivial applications.
Students and researchers in geometry and analysis are warmly invited.
Students may register to obtain credit for this course (MATX72ZL Advanced Study of Nonlinear Mechanics).
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Schedule:
Thursday 29 June 10:4012:10
Monday 3 July 13:0014:30
Thursday 6 July 10:4012:10
Monday 10 July 13:0014:30
Thursday 13 July 10:4012:10
Monday 17 July 13:0014:30
Thursday 20 July 10:4012:10 [to be confirmed]
Monday 24 July 13:0014:30 [to be confirmed]
The main topics will be:
1. The Mean field equation without singular sources l : sharp estimate
2. The Mean field equation without singular sources ll: topological degree
3. The Mean field equation with singular sources at critical values of the parameter
4. The Mean field equation, the generalized Lame equation and the Painleve VI
equation l: the Hitchin case
5. The Mean field equation, the generalized Lame equation and the Painleve VI
equation ll: an application to the Painleve VI equation