Mathai studied at
Bishop Cotton Boys' School, Bangalore. Mathai received a
BA at the
Illinois Institute of Technology. He then proceeded to the
Massachusetts Institute of Technology, where he was awarded a
doctorate under the supervision of
Daniel Quillen, a
Fields Medallist. Mathai's work is in the area of
geometric analysis. His research interests are in L^2 analysis, index theory, and
noncommutative geometry. He currently works on mathematical problems that have their roots in physics, for example, topological field theories,
fractional quantum Hall effect, and
D-branes in the presence of
B-fields. The main focus of his research is on the application of noncommutative geometry and index theory to mathematical physics, with particular emphasis on
string theory. His current work on index theory is ongoing joint work with
Richard Melrose and
Isadore Singer, on the fractional analytic index and on the index theorem for projective families of elliptic operators. His current work on string theory is ongoing joint work with Peter Bouwknegt, Jarah Evslin, Keith Hannabuss and
Jonathan Rosenberg, on T-duality in the presence of background flux. The Mathai–Quillen formalism appeared in
Topology, shortly after Mathai completed his Ph.D. Using the
superconnection formalism of Quillen, they obtained a refinement of the
Riemann–Roch formula, which links together the
Thom classes in
K-theory and
cohomology, as an equality on the level of differential forms. This has an interpretation in physics as the computation of the classical and quantum (super)
partition functions for the fermionic analogue of a
harmonic oscillator with source term. In particular, they obtained a nice
Gaussian shape representative of the
Thom class in cohomology, which has a peak along the zero section. Its universal representative is obtained using the machinery of
equivariant differential forms. Mathai was awarded the
Australian Mathematical Society Medal in 2000. From August 2000 to August 2001, he was also a
Clay Mathematics Institute Research Fellow and visiting scientist at the
Massachusetts Institute of Technology. From March to June 2006, he was a senior research fellow at the
Erwin Schrödinger Institute in Vienna. ==Selected publications==