目：Local mass and a priori estimate for singular Toda system

间：2022.06.17（星期五）14:30-15:30

点：腾讯会议：389-743-322

要：In this talk, we will discuss the local masses of Toda system with n≥2 . By using Pohozaev identity, the monodromy theory from complex ODE and some recent work by Eremenko-Gabrielov-Tarasov, we are able to determine the local masses for the system and it turns out that the local masses are closely related to the element in the Weyl group of the corresponding Lie algebra. Based on this quantization result, the a priori estimate and some existence results of this system are obtained.

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目：Szego Limit Theorem and “Mean Field Equations”

间：2022.06.17（星期五）15:30-16:30

点：腾讯会议：389-743-322

要：In this talk, we will review the classic Lebedev Milin inequality and Szego limit theorem on S1. PDE approach is adopted to establish infinitely many inequalities involving higher order “moments” through classifying the solutions of “Mean field equation” on S1. Higher dimensional analogues will be mentioned if time permits.