The Hyamfest

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.

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