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)
--
*Dr. Matthew Badger*, Assistant Professor
Department of Mathematics, University of Connecticut
www.math.uconn.edu/~badger/
