THEMATIC PROGRAM
UNLIKELY INTERSECTIONS,
HEIGHTS, AND EFFICIENT
CONGRUENCING
In recent years there has been a
great deal of success in applying
methods of analytic number theory to
questions of arithmetic geometry. This
thematic program focussed on three
topics: o-minimality, heights, and
“efficient congruencing” and featured
two graduate courses, a mini-course,
three workshops, and a post-doctoral
seminar.
The two graduate courses were taught by Patrick Ingram
and myself. My own course was designed mostly to serve as
background for unlikely intersections, which is a topic that
underpins a large part of the program. One enticing feature
Workshop in efficient congruencing and translation-invariant systems
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about this subject is that it brings together several different
fields, so this course was designed to acquaint everyone
with the background they were missing. Patrick Ingram’s
course on Arithmetic Dynamics was extremely interesting as
a developing subject that has more and more to say about
unlikely intersections. This was evident during our very first
workshop in a wonderful talk by Laura Demarco, when she
explained how to prove new and old results on simultaneous
torsion. I know of at least one graduate student at Toronto
who is now working with Patrick as a result of the course.
There was also a nine-hour mini course taught jointly by
Trevor Wooley and Yu Ru-Liu. These were very well attended
and explained the Hardy-Littlewood method as well as the
refinements provided by the efficient congruencing method,
and how it can be used to improve bounds on the Waring
problems.