In this series of talks, I will introduce some non-linear methods in circle packing theory. The following are three main topics: 1. Maximum theorem and variational principle; 2. Continuity method and topological degree; 3. Intersection number theory. Applying these methods, we shall obtain many interesting consequences, such as Birkhoff’s billiard theorem, Circle packing theorem, Koebe’s circle domain theorem, Midscribability theorem, and so on. If time permits, I will also introduce the flow method to find the solutions.

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