Karl Schwede<br>
Title:  F-singularities in families<br>

Abstract:  F-singularities are classes of singularities defined
by the behavior Frobenius.  A prominent tool for measuing these
singularities is the test ideal, a characteristic p > 0 analog
of the
multiplier ideal.
Recently, there has been interest in applying the methods of
F-singularities to a number of geometric problems in positive
characteristic.  However, one gap in the theory has been the
behavior of
F-singularities in families.  For example restriction theorems
for test
ideals have been lacking.

In this talk, I will discuss recent joint work with Zsolt
Patakfalvi and
Wenliang Zhang on the behavior of F-singularities and test
ideals in
families.  For example, we will obtain generic (and
non-generic)
restrictions theorems for test ideals.  Some global geometric
consequences will also be discussed if there is sufficient time