Robert Bartnik (1956-2022) was an Australian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

based at

Monash University Monash University () is a public research university based in Melbourne, Victoria, Australia. Named for prominent World War I general Sir John Monash, it was founded in 1958 and is the second oldest university in the state. The university h ...

. He is known for his contributions to the rigorous mathematical study of

general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...

. He received his bachelor's and master's degrees from

Melbourne University The University of Melbourne is a public research university located in Melbourne, Australia. Founded in 1853, it is Australia's second oldest university and the oldest in Victoria. Its main campus is located in Parkville, an inner suburb no ...

and a PhD in mathematics from

Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ...

in 1983, where his advisor was

Shing-Tung Yau Shing-Tung Yau (; ; born April 4, 1949) is a Chinese-American mathematician and the William Caspar Graustein Professor of Mathematics at Harvard University. In April 2022, Yau announced retirement from Harvard to become Chair Professor of mathem ...

. In 2004 he was elected to the Australian Academy of Science, with citation: His work with John McKinnon has been widely studied in the physics literature. They show that there is a discrete set of static solutions to the coupled Einstein/Yang-Mills equations which are geodesically complete and asymptotically flat. This is interesting since such solutions are known not to exist in the cases of the Einstein vacuum equations, the coupled Einstein/Maxwell equations, and the Yang-Mills equations. Although Bartnik and McKinnon's work was numerical, their observed phenomena has been mathematically justified by Joel Smoller, Arthur Wasserman,

, and Joel McLeod. In the mathematics literature, he is known for his work with

Leon Simon Leon Melvyn Simon , born in 1945, is a Leroy P. Steele PrizeSee announcemen retrieved 15 September 2017. and Bôcher Memorial Prize, Bôcher Prize-winningSee . mathematician, known for deep contributions to the fields of geometric analysis, g ...

on solving the Dirichlet problem for prescribed

mean curvature In mathematics, the mean curvature H of a surface S is an ''extrinsic'' measure of curvature that comes from differential geometry and that locally describes the curvature of an embedded surface in some ambient space such as Euclidean space. The ...

, in the setting of spacelike hypersurfaces of

Minkowski space In mathematical physics, Minkowski space (or Minkowski spacetime) () is a combination of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the iner ...

. His most widely cited work is on the geometric and analytic study of the ADM mass. He shows that it is geometrically defined by constructing "optimal" asymptotically flat coordinates, and gives an extension of

Edward Witten Edward Witten (born August 26, 1951) is an American mathematical and theoretical physicist. He is a Professor Emeritus in the School of Natural Sciences at the Institute for Advanced Study in Princeton. Witten is a researcher in string theory, q ...

's proof of the time-symmetric

positive energy theorem The positive energy theorem (also known as the positive mass theorem) refers to a collection of foundational results in general relativity and differential geometry. Its standard form, broadly speaking, asserts that the gravitational energy of a ...

to the higher-dimensional spin setting. He was a visiting scholar at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent schola ...

in 1980-81.Institute for Advanced Study: A Community of Scholars

Major publications

As of 2022, Bartnik has been the author of around 30 research articles. The following publications are among the best-known: * * * * * His collected works were published in 2021: *

References

* * * Fellows of the Australian Academy of Science Institute for Advanced Study visiting scholars Mathematicians from Melbourne Living people University of Melbourne alumni Princeton University alumni Year of birth missing (living people) {{mathematician-stub