A lifetime of mathematical achievement recognised

Full article issued by The University of Adelaide and the Australian Academy of Science.

ARC Australian Laureate Fellow, Sir Thomas Elder Professor Mathai Varghese FAA, from The University of Adelaide's School of Mathematical Sciences, has been awarded the prestigious Hannan Medal by the Australian Academy of Science for his career-long outstanding contributions in the field of geometric analysis.

A partial citation for the Hannan Medal reads: 'Professor Mathai Varghese has made highly influential contributions to the field of geometric analysis, which relates geometric, analytic and algebraic properties of (possibly infinite dimensional) manifolds. Among these are his co-inventions of Fractional Index Theory and Projective Index Theory that have received international recognition for explaining the mystery of the analytic counterpart of the A-hat genus. His recent joint work extending the Fractional Index Theorem to infinite dimensional loop spaces is itself of immense significance.'

Professor Varghese taught himself advanced mathematics by borrowing books on geometry topology from Bangalore's British Council library, which was far in advance of his high school curriculum. He completed his PhD at the Massachusetts Institute of Technology in 1986 and was a postdoctoral researcher at the University of Chicago, before joining The University of Adelaide in 1989, where he has led a number of ARC grants and fellowships. He was a Clay Mathematics fellow at the Massachusetts Institute of Technology in 2000-2001.

Professor Varghese's research area is index theory, which helps in the understanding of elliptic differential equations – which arise in the mathematical modelling of many problems in the real world.

'Although solutions to differential equations are very difficult to find, it is comparatively much easier to calculate the index without even knowing the solution to the differential equation,' says Professor Varghese.

His work has myriad applications both within mathematics, and to mathematical physics, such as condensed matter physics and the 'theory of everything' known as string theory. Since moving to Adelaide, Professor Varghese has published seminal articles cited the world over, and his work is considered critical to our understanding of geometry, topology and elliptic differential equations in both finite and infinite dimensions.