The conference and workshop Geometry & Topology Down Under consisted of
two exciting weeks of lectures and research talks in the Department of Mathemat-
ics and Statistics at the University of Melbourne. The event brought together an
impressive line-up of guests from the United States, Europe and Asia, and was
attended by 115 students and researchers. It attracted experts and emerging re-
searchers who reported on recent results and explored future directions in Geometry
and Topology. The conference was held in honour of Hyam Rubinstein and cele-
brated his contributions to topology and his long-standing role as an advocate for
the mathematical sciences.
The workshop (11-15 July) and conference (18-22 July) covered a broad range of
topics in Geometry and Topology, including hyperbolic and symplectic geometry,
Heegaard splittings and triangulations of 3-manifolds, and recent advances and
applications in the study of graph manifolds. The organisers interpreted the topic
of the workshop and conference broadly, so that the meeting had appeal to group
theorists, analysts, differential geometers and low-dimensional topologists. The
event was designed so that it was beneficial not only to the experts in the field but
also to early career researchers and graduate students.
In the first week, short courses were given by Danny Calegari on Ergodic Theory
of Groups, Walter Neumann on Invariants of hyperbolic 3–manifolds and Leonid
Polterovich on Function theory on symplectic manifolds. The short courses intro-
duced honours and postgraduate students, as well as early-career or established
researchers, to a broad range of methods and results. Each lecturer gave a 75-
minute lecture each day. Discussion sessions, which were led by vibrant, early-
career researchers, were held each afternoon. The lectures were of exceptionally
high standard, and special notes and exercises were designed for the participants.
All lectures have been recorded and are, in addition to a wealth of other material,
available on the conference website: www.ms.unimelb.edu.au/∼hyamfest.
The conference in the second week featured a line-up of 23 international experts
who reported on a variety of new results. For instance, Ian Agol gave a proof of
Simon’s conjecture, David Gabai reported on recent progress on the topology of
ending lamination space, Walter Neumann talked about a new geometric decom-
position for complex surface singularities, Yi Ni showed that Khovanov homology
with an extra module structure detects unlinks, and Gang Tian described a new
symplectic curvature flow. Moreover, each day featured a “What is...?” talk in
the spirit of the Notices of the AMS just before lunch. These talks were positively
received by both junior and senior researchers.