**“Zero-Sets
of Functions in Bergman Spaces****”**

By

**BERK BAVAŞ**

**(BİLKENT UNIVERSITY)**

**Abstract:**** ** This is a Senior Project presentation

The Bergman space A^p consists of
all holomorphic functions defined in the unit disc the p-th power of whose
complex modulus is integrable with respect to the area measure. We say
{z_k} is an A^p zero-set if and only if there exists a function f in A^p such
that f vanishes precisely on this set. In this talk we will discuss
properties of A^p zero-sets. For this purpose the following three questions
will be answered: Do A^p zero sets vary
with p? In other words, does there exist an A^q zero-set that is not an
A^p zero-set for two positive real numbers p and q? Is the union of two A^p zero-sets an A^p
zero-set? Must every subset of an A^p
zero-set be an A^p zero set? I will
mainly follow Charles Horowitz's 1974 work in which all three questions are
answered.

**Date: ****Tuesday, December 23, 2014**

**Time: ****15:40**

**Place: ****Mathematics Seminar Room,
SA-141**

Tea and cookies will be served before the
seminar.