Mathematics Colloquia and Seminars

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In the pre-talk, we review the Bergman kernel and metric and their variational properties, and use them to degenerate Riemann surfaces, give a new proof of Suita's conjecture, and characterize domains by curvatures.

In the second part, we focus on $L^2$ existence and extension theorems, and use weighted $L^2$ approach to obtain sharp pointwise and uniform estimates for Cauchy-Riemann equations on certain symmetric spaces including Cartan classical domains and polydiscs.