Information AboutMathai Varghese |
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BIOGRAPHY Varghese received his 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 Quillen, a Fields Medallist . Varghese's work may be considered to fall under the ambit of Geometric Analysis . His research interests are in 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 . The Mathai–Quillen formalism appeared in Topology shortly after Varghese completed his PhD. 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 Shaped 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 . Varghese was awarded the Australian Mathematical Society Medal in 2000. From August 2000 to August 2001, he was also a Research Scholar and Visiting Scientist at the Clay Mathematics Institute . EXTERNAL LINKS
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