The theory of locally compact groups stretches out between two opposite poles.
The first pole consists of Lie groups, which form a prominent family,
subjected to a rich and deep structure theory including a complete classification of the simple groups.
Since the solution of Hilbert's fifth problem in the 1950's,
it is moreover known that the realm of Lie theory extends to all connected locally compact groups.
The opposite pole is that of discrete groups,
subjected to all kinds of wild phenomena and pathological behaviours.
The large open area lying between those two poles is still mysterious to a large extent;
it has however been observed recently that the very existence of a non-discrete topology tends
to impose strong algebraic restrictions.
It has moreover become clear that relevant tools for the exploration of that area
pertain to various fields, including geometric group theory, profinite group theory, ergodic theory,
abstract harmonic analysis, and model theory.
It is the goal of the conference to bring together experts from those fields,
on the basis of a common sensitivity to locally compact groups beyond the cases of Lie or discrete groups.
The conference will thus provide an opportunity to establish the current state of the art,
to identify the major challenges for future investigations,
and hopefully to create new connections and interactions between the different fields mentioned above.