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Matthew is an astrophysicist that uses the world's largest radio telescopes to discover neutron stars and use them to test theories of gravity and stellar evolution. His group is known for designing supercomputers to process radio data and conducting some of the most precise measurements ever performed using millisecond pulsars, a bizarre form of star that rotate up to 700 times per second. In 2011 his group was part of a team that discovered the diamond planet orbiting the pulsar J1719-1438.

Matthew was the founding Director of the Centre for Astrophysics and Supercomputing at Swinburne University of Technology from its inception in 1998 until 2010.

He is currently Swinburne's Pro-Vice Chancellor for Research and the head of the Dynamic Universe theme of the ARC Centre of Excellence in All-Sky Astrophysics (CAASTRO).