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Plenary lectureSuita conjecture and the Ohsawa--Takegoshi extension theorem |
Zbigniew Błocki, Jagiellonian University, Poland
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Suita conjecture (1972) asked for the optimal lower bound for the
Bergman kernel in terms of logarithmic capacity for domains on the
plane. As observed by Ohsawa in the 90's, it is closely related to
the \(L^2\)-extension problem for holomorphic functions of several
variables. It was eventually proved using techniques of the
$ {\bar{\partial}} $-equation and Hörmander's \(L^2\)-estimate. We will
present some generalizations of the Suita conjecture in higher
dimensions. One of interesting aspects is a relation to the Mahler
conjecture and the Bourgain-Milman inequality in convex analysis,
mostly thanks to a recent complex analytic proof of the latter by
Nazarov.
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