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Gabor Szekelyhidi : Extremal Kahler metrics and the Yau-Tian-Donaldson conjecture

I will first explain with a few simple examples a beautiful picture in geometric invariant theory which relates quotient constructions in symplectic and algebraic geometry. Then we will naively apply this picture in a suitable infinite dimensional setting, leading us to the notion of extremal Kahler metrics and the Yau-Tian-Donaldson conjecture, which is an important problem in Kahler geometry today.

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