Professor, Department of Pure Mathematics, Adelaide University, Australia. Australian Research Council Senior Research Fellow.
Mathai Varghese is a major contributor in the field of geometric analysis. His research interests are in L2 analysis, index theory and noncommutative geometry. Several mathematical problems that he currently works on originate from physics, for example topological field theories, fractional quantum Hall effect, D-branes in the presence of B-fields and T-duality in string theory in the presence of background B-fields.
His main project is on the applications of noncommutative geometry and index theory to mathematical physics, with particular emphasis on string theory and the fractional quantum Hall effect.
2000 Australian Mathematical Society Medal.
2000-2001 Clay Mathematics Institute Research Scholar and Visiting Scientist at the Massachusetts Institute of Technology.
2006 Senior Research Fellow at the Erwin Schrodinger Institute, Vienna.
Fractional Analytic Index, (with R.B. Melrose and I.M. Singer), (2004), 22 pages [math.DG/0402329]
T-duality for torus bundles with H-fluxes via noncommutative topology, II: the high-dimensional case and the T-duality group (with J. Rosenberg), 36 pages, Advances in Theoretical and Mathematical Physics, 10 no. 1 (2006) [hep-th/0508084]
Nonassociative tori and applications to T-duality (with P. Bouwknegt and K. Hannabuss), Communications in Mathematical Physics, 264 no. 1 (2006) 41-69
On a generalized Connes-Hochschild-Kostant-Rosenberg theorem, (with Danny Stevenson), Advances in Mathematics, 200 no. 2 (2006) 303-335.
T-duality for torus bundles via noncommutative topology (with J. Rosenberg), Communications in Mathematical Physics, 253 no. 3 (2005) 705-721. [hep-th/0401168]
The index of projective families of elliptic operators, (with R.B. Melrose and I.M. Singer), Geometry and Topology, 9 (2005) 341-373.
On the Topology and Flux of T-Dual Manifolds (with P. Bouwknegt and J. Evslin), Physical Review Letters, 92, 181601 (2004)
Equivalence of spectral projections in semiclassical limit and a vanishing theorem for higher traces in K-theory, (with Y. Kordyukov and M.A. Shubin), J. Reine Angew. Math. (Crelle Journal), 581 (2005) 193 - 236.
Approximating L2-invariants and the Atiyah conjecture (with J. Dodziuk, P. Linnell, T. Schick and S. Yates), Communications on Pure and Applied Mathematics, 56, no. 7, (2003), 839-873.
Twisted index theory on good orbifolds,II: fractional quantum numbers, (with M. Marcolli) Communications in Mathematical Physics, 217, no.1 (2001) 55-87.
Quantum Hall effect on the hyperbolic plane in the presence of disorder (with A. Carey, K. Hannabuss), Lett. Math. Phys., 47 (1999) 215-236.
K-theory of twisted group C*-algebras and positive scalar curvature, Rothenberg Festschrift, Contemporary Mathematics, 231 (1999) 203-225.
Quantum Hall Effect on the hyperbolic plane, (with A. Carey, K. Hannabus and P. McCann), Communications in Mathematical Physics, 190 No. 3 (1998) 629-673.
Determinant Lines, Von Neumann algebras and L2 torsion(with A. Carey and M. Farber),J. Reine Angew. Math. (Crelle Journal), 484 (1997) 153-181.
Equivariant holomorphic Morse inequalities: a heat kernel proof (with S. Wu), J. Differential Geometry, 46 (1997) 78-98.
Spectral flow, eta invariants, and von Neumann algebras, J. Functional Analysis, 109 (1992), no. 2, 442--456.
L2-analytic torsion. J. Functional Analysis, 107 (1992), no. 2, 369--386.
Superconnections, Thom classes and equivariant differential forms, (with D. Quillen), Topology 25 (1986), 85–110.