Local Maass forms and theta lifts

In this talk, we consider local Maass forms.  These are functions which locally
satisfy the differential equation of a Maass form away from certain geodesics
of measure zero.  In joint work with Bringmann and Kohnen, a first natural
subclass of these has been discovered and linked to the Shimura and Shintani
lifts, as will first be described in this talk.  We then determine that these
functions are theta lifts of weak Maass forms, explaining many of the
properties previously discovered.  This is based upon joint work with Bringmann
and Kohnen and Bringmann and Viazovska.