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The Pick interpolation problem


Title : The Pick interpolation problem.
Speaker : Prof. Gautam Bharali, IISc Bangalore.
Date : 23/03/2022, 05:30 PM , Online Mode.


The Pick interpolation problem asks — given two finite ordered sets S and T of the same cardinality in the open unit disc — if one can tell just by looking at S and T whether or not there is a holomorphic self-map of the open unit disc that maps the j-th point in S to the j-th point in T. The Schwarz-Pick lemma tells us that such a map isn’t always available even if S and T contain only two points. In this talk, I shall first try to survey why one is interested in a puzzle like this. Next, we shall examine the (very pretty) solution to this problem. This talk will be accessible to anyone who is familiar with the Schwarz lemma in complex analysis.