  We present a list of problems in arithmetic topology posed at the June 2019
PIMS/NSF workshop on "Arithmetic Topology". Three problem sessions were hosted
during the workshop in which participants proposed open questions to the
audience and engaged in shared discussions from their own perspectives as
working mathematicians across various fields of study. Participants were
explicitly asked to provide problems of various levels of difficulty, with the
goal of capturing a cross-section of exciting challenges in the field that
could help guide future activity. The problems, together with references and
brief discussions when appropriate, are collected below into three categories:
1) topological analogues of arithmetic phenomena, 2) point counts, stability
phenomena and the Grothendieck ring, and 3) tools, methods and examples.
