Today's seminar will feature a talk by Malik Younsi from Stony Brook University. Malik will speak on geometric function theory (full title and abstract below). See you this afternoon!
P.S. We will go to dinner with the speaker tonight (possibly Chang's). Everyone is welcome to attend.
Seminar Time & Location: 3:30pm in MSB 109A
Title: On the analytic and Cauchy capacities
Abstract:
Analytic capacity of compact plane sets was first introduced by
Ahlfors in order to study Painlev\'e's problem of finding a geometric
characterization of the compact sets that are removable for bounded
holomorphic functions. Despite recent advances due to Tolsa, the
properties of analytic capacity remain rather mysterious. In particular,
it is still unknown if analytic capacity is equal to the so-called
Cauchy capacity. In this talk, I will present some new sufficient
conditions for a compact planar set to have equal analytic and Cauchy capcities. As a consequence, I will describe how to
produce examples of compact plane sets such that the above equality
holds but the Ahlfors function is not the Cauchy transform of any
complex Borel measure supported on the set.
Current & Upcoming Seminar Talks
March 27 - Malik Younsi (Stony Brook University)
April 10 - Robert Neel (Lehigh University)
April 17 - Tess Anderson (Brown University)
April 24 - Alexander Roitershtein (Iowa State University)
May 1 - Samuel Watson (MIT)
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