The workshop
"Counting Points on Varieties" consisted of two parts.

The first
week, April 14--17, was a so called Stieltjesweek,
aimed at high-level masters students, graduate students, and beginning postdocs. There were three mini-courses: one on the Birch
and Swinnerton-Dyer conjecture, another on Zeta
functions, Laplacians, and étale
cohomology, and a third on the Batyrev-Manin
conjecture. Each morning there was a one-hour lecture on each of the three
topics, while the participants worked on exercises during the afternoon, which they
presented to each other, each day at 16.00.

Tim Dokchitser taught the course on the Birch and Swinnerton-Dyer conjecture, one of the famous one-million
dollar millennium problems. It relates the rank of the Mordell-Weil
group of an elliptic curve to the order of vanishing of its associated
L-series. He focused mostly on the parity conjecture, which follows from the
Birch and Swinnerton-Dyer conjecture. There is no
reason to believe the parity conjecture is easier to prove, but it is more
easily accessible, especially in a short course.

Ted Chinburg taught the course on Zeta functions, Laplacians, and étale cohomology. He presented a wide variety of related
problems, including the question whether you can hear the shape of a drum.

Ronald van Luijk taught the course on the Batyrev--Manin conjecture, which predicts the asymptotic growth of
the number of rational points of bounded height on certain varieties in terms
of the bound.

The courses
were well received by the students, who almost all (around 40) participated
very actively in the exercises and the presentation of the solutions. Thursday
night there was a well-attended dinner where all students from various
countries (

in a nonmathematical manner.

Based on the
responses from the students, we consider the week a big success.

The second
part was a week-long research workshop.
About 20 talks were given by experts in one of several fields, all
related to the “counting points on varieties'' theme. In total about 60 people attended
the workshop, amongst them were many participants of the first, instructional,
week and other young mathematicians.

The speakers
were very well aware of the broad nature of this workshop and consistently went
through a lot of effort to communicate to the whole audience, and not just to
those most familiar with their topic. Also this made it easier for the
attending students to connect some of these talks with what they had learnt in
the first week of the workshop.

With only four
one-hour talks per day, the program was designed to allow ample space for
informal discussion during the breaks. This opportunity was used intensively
and it was not uncommon to find mathematicians of the highest reputations
(Stephen Lichtenbaum, Jean-Pierre Serre)
discuss mathematics with young mathematicians during the breaks.

Almost
everybody was present for the conference dinner which was held on Wednesday
evening, on a boat making a tour of the Groene Hart.

The conference
ended with two talks on Friday morning, given by renowned mathematicians Carl Pomerance and Manjul Bhargava. These talks formed also the beginning of the
day-long festivities organized for Hendrik Lenstra's sixtieth birthday. On top of the workshop participants,
about 50 mathematicians mostly from the