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I will give a series of 3 lectures; in the first 2 lectures the student will experience a rapid course in Riemannian geometry, among other things, which will be useful towards understanding geometric side of complex analysis. Then in the 3rd lecture, I will present the semicontinuity theorem which is a research subject of current interest.

If students are familiar with basics of Riemannian and Kaehlerian geometry, I can skip some of the material of the 1st lecture.