Lorentz Center

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## Logic and Random Graphs |

Random graphs are mathematical models of
networks that have been studied intensively for over half a century, beginning
with the seminal work of Erdős and Rényi. Given the central position of logic within
graph theory and theoretical computer science, it comes as no surprise that
researchers have studied random graphs from a logical perspective for nearly as
long as random graph theory has existed.
Despite its established role within random graph theory, there is a
strong, renewed impetus for research activity on random graphs from a logical
perspective. This is partly because recent advances in our understanding of
various random graph models, including random graphs with a given degree
distribution and random graphs embeddable on surfaces, make it possible to
attack questions that were out of reach until very recently. Another reason for the renewed impetus is
related to graph limits. After the introduction of graph limits around 2006,
many in the field realized that there is a close connection between graph
limits and some of the phenomena and in particular the limit objects produced
in the theory of logical limit laws of random graphs. In this five-day workshop, we gathered
together some of the most active and influential researchers in the field, with
roughly equal proportions of participant working mostly on random graphs, logic
or theoretical computer science, and visiting from several parts of North
America and Europe. There were twenty talks spread over five
days, which left ample time for (informal) discussions. This appears to have
been appreciated by the participants. On Monday there was an open problem
session. Several of the participants are now working on the problems posed by
others, and one of the open problems was even solved during the workshop.
Another nice, concrete result of the workshop was that one of the keynote
speakers, Prof. Luczak, managed to solve an old
research problem while preparing his presentation. The workshop provided a useful platform to
view future directions for research in the area. Given the even mix of younger
and more established scientists, and of different fields, it was an excellent
opportunity for many parties to gain new perspectives. We are grateful to have received additional
support from KNAW, NWO and STAR, which greatly contributed to the success of
the event.
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