Source: https://researchers.adelaide.edu.au/profile/mathai.varghese
Timestamp: 2019-04-26 08:35:02+00:00

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Professor Mathai Varghese is well-known internationally for his research in geometric analysis and mathematical physics. He completed his PhD at the Massachusetts Institute of Technology in 1986. He was a postdoc (Dickson Instructor) at the University of Chicago and since 1989, he has been at the University of Adelaide in varying ARC Postdoctoral positions, and was appointed Professor of Pure Mathematics in 2006 and the Elder Chair in Mathematics in 2013.
The quality of Professor Varghese’s research has been recognised with awards over the years (see below) including election to the Australian Academy of Science in 2011 and award of the prestigious Australian Laureate Fellowship (2018-2022). Professor Varghese has published over 100 scientific articles and has been awarded many ARC awards (Large Grants, Discovery Projects and Fellowships).
Professor Varghese has been very active in national leadership roles, including membership in sectional committee 1 of the Australian Academy of Science, various prize committees of the Australian Academy of Science and the Australian Mathematical Society. From 2006-2009, he was the Vice President (in charge of annual conferences) of the Australian Mathematical Society and also a member of the Steering Committee.
My recent research interests include: index theory of elliptic operators; secondary invariants of elliptic operators; geometric quantization: noncompact context; and noncommutative geometry. Recently my interests include gauge theory as well as topological obstructions to the existence of positive scalar curvature metrics on compact spin manifolds.
Several mathematical problems that I currently work on originate from physics, for example: topological field theories, Mathematics of Condensed matter physics:(fractional) quantum Hall effect 1985 & 1998 Nobel Prizes in Physics; topological insulators http://iopscience.iop.org/journal/1751-8121/labtalk/article/63194 ; topological semimetals https://jphysplus.iop.org/2017/02/24/3d-topological-semimetals/, 2016 Nobel Prize in Physics; Mathematics of string theory & duality in a background flux.
2018 Guo, H., Varghese, M., & Wang, H. (2018). Positive scalar curvature and Poincaré duality for proper actions. Journal of Noncommutative Geometry.
2018 Han, F., & Mathai, V. (2018). T-duality in an H-Flux: exchange of momentum and winding. Communications in Mathematical Physics, 363(1), 333-350.
2018 Varghese, M., & Rosenberg, J. (2018). Group dualities, T-dualities, and twisted K-theory. Journal of the London Mathematical Society, 97(1), 1-23.
2018 Linshaw, A., & Mathai, V. (2018). T-duality of singular spacetime compactifications in an H-flux. Journal of Geometry and Physics, 129, 269-278.
2018 Benameur, M., & Varghese, M. (2018). Gap-labelling conjecture with nonzero magnetic field. Advances in Mathematics, 325, 116-164.
2018 Hannabuss, K., Mathai, V., & Thiang, G. (2018). T-duality simplifies bulk-boundary correspondence: the noncommutative case. Letters in Mathematical Physics, 108(5), 1163-1201.
2018 Bouwknegt, P., Evslin, J., & Mathai, V. (2018). Spherical T-Duality and the spherical Fourier-Mukai transform. Journal of Geometry and Physics, 133, 303-314.
2017 Varghese, M., & Thiang, G. (2017). Differential topology of semimetals. Communications in Mathematical Physics, 355(2), 561-602.
2017 Mathai, V., & Thiang, G. (2017). Global topology of Weyl semimetals and Fermi arcs. Journal of Physics A: Mathematical and Theoretical, 50(11), 1-11.
2017 Hochs, P., & Mathai, V. (2017). Quantising proper actions on SpinC-manifolds. Asian Journal of Mathematics, 21(4), 631-686.
2017 Mathai, V., & Melrose, R. (2017). Geometry of pseudodifferential algebra bundles and fourier integral operators. Duke Mathematical Journal, 166(10), 1859-1922.
2016 Mathai, V., & Thiang, G. (2016). T-Duality simplifies bulk-boundary correspondence. Communications in Mathematical Physics, 345(2), 675-701.
2016 Mathai, V., & Thiang, G. (2016). T-Duality simplifies bulk–boundary correspondence: some higher dimensional cases. Annales Henri Poincare, 17(12), 3399-3424.
2016 Hannabuss, K., Mathai, V., & Thiang, G. (2016). T-duality simplifies bulk-boundary correspondence: the parametrised case. Advances in Theoretical and Mathematical Physics, 20(5), 1193-1226.
2016 Hochs, P., & Varghese, M. (2016). Formal geometric quantisation for proper actions. Journal of Homotopy and Related Structures, 11(3), 409-424.
2016 Hochs, P., & Mathai, V. (2016). Spin-structures and proper group actions. Advances in Mathematics, 292, 1-10.
2015 Linshaw, A., & Varghese, M. (2015). Twisted chiral de Rham complex, generalized geometry, and T-duality. Communications in Mathematical Physics, 339(2), 663-697.
2015 Hochs, P., & Mathai, V. (2015). Geometric quantization and families of inner products. Advances in Mathematics, 282, 362-426.
2015 Bouwknegt, P., Evslin, J., & Mathai, V. (2015). Spherical T-duality II: an infinity of spherical T-duals for non-principal SU(2)-bundles. Journal of Geometry and Physics, 92, 46-54.
2015 Mathai, V., & Sati, H. (2015). Higher abelian gauge theory associated to gerbes on noncommutative deformed M5-branes and S-duality. Journal of Geometry and Physics, 92, 240-251.
2015 Bouwknegt, P., Evslin, J., & Mathai, V. (2015). Spherical T-duality. Communications in Mathematical Physics, 337(2), 909-954.
2015 Han, F., & Mathai, V. (2015). Exotic twisted equivariant cohomology of loop spaces, twisted Bismut–Chern character and T-duality. Communications in Mathematical Physics, 337(1), 127-150.
2015 Benameur, M. T., & Mathai, V. (2015). Spectral sections, twisted rho invariants and positive scalar curvature. Journal of Noncommutative Geometry, 9(3), 821-850.
2015 Varghese, M., & Thiang, G. (2015). T-duality of topological insulators. Journal of Physics A: Mathematical and Theoretical, 48(42), 42FT02-1-42FT02-10.
2014 Mathai, V., & Rosenberg, J. (2014). T-duality for circle bundles via noncommutative geometry. Advances in Theoretical and Mathematical Physics, 18(6), 1437-1462.
2014 Benameur, M., & Mathai, V. (2014). Index type invariants for twisted signature complexes and homotopy invariance. Mathematical Proceedings of the Cambridge Philosophical Society, 156(3), 473-503.
2014 Benameur, M., & Mathai, V. (2014). Corrigendum to "Conformal invariants of twisted Dirac operators and positive scalar curvature" [J. Geom. Phys. 70 (2013) 39-47]. Journal of Geometry and Physics, 76, 263-264.
2013 Dey, R., & Varghese, M. (2013). Holomorphic Quillen determinant line bundles on integral compact Kähler manifolds. Quarterly Journal of Mathematics, 64(3), 785-794.
2013 Bernameur, M., & Varghese, M. (2013). Conformal invariants of twisted Dirac operators and positive scalar curvature. Journal of Geometry and Physics, 70, 39-47.
2012 Hekmati, P., & Varghese, M. (2012). T-duality of current algebras and their quantization. Contemporary Mathematics, 584, 17-37.
2012 Varghese, M., & Wu, S. (2012). Topology and Flux of T-Dual Manifolds with Circle Actions. Communications in Mathematical Physics, 316(1), 279-286.
2012 Hannabuss, K., & Varghese, M. (2012). Nonassociative strict deformation quantization of C*-algebras and nonassociative torus bundles. Letters in Mathematical Physics, 102(1), 107-123.
2012 Bouwknegt, P., Varghese, M., & Wu, S. (2012). Bundle gerbes and moduli spaces. Journal of Geometry and Physics, 62(1), 1-10.
2011 Varghese, M., & Wu, S. (2011). Analytic torsion for twisted de Rham complexes. Journal of Differential Geometry, 88(2), 297-332.
2011 Mahanta, S., & Varghese, M. (2011). Operator algebra quantum homogeneous spaces of universal gauge groups. Letters in Mathematical Physics, 97(3), 263-277.
2011 Hannabuss, K., & Varghese, M. (2011). Parameterized strict deformation quantization of C*-bundles and Hilbert C*-modules. Journal of the Australian Mathematical Society, 90(1), 25-38.
2011 Varghese, M., & Rosenberg, J. (2011). A noncommutative sigma-model. Journal of Noncommutative Geometry, 5(2), 265-294.
2011 Asghari, A. (2011). Psychometric properties of a modified version of the Roland-Morris disability questionnaire (M-RMDQ).. Archives of Iranian medicine, 14(5), 327-331.
2010 Mathai, V., Melrose, R., & Singer, I. (2010). The index of projective families of elliptic operators: The decomposable case. Asterisque, 328, 1-35.
2010 Varghese, M., & Zhang, W. (2010). Geometric quantization for proper actions. Advances in Mathematics, 225(3), 1224-1247.
2010 Varghese, M., & Wu, S. (2010). Twisted analytic torsion. Science China Mathematics, 53(3), 555-563.
2009 Varghese, M., Melrose, R., & Singer, I. (2009). The index of projective families of elliptic operators: the decomposable case. Asterisque, 328(328), 255-296.
2009 Chakraborty, P., & Varghese, M. (2009). The geometry of determinant line bundles in noncommutative geometry. Journal of Noncommutative Geometry, 3(4), 559-578.
2009 Green, R., & Varghese, M. (2009). Harmonic Cheeger-Simons characters with applications. Journal of Geometry and Physics, 59(5), 663-672.
2009 Bouwknegt, P., & Varghese, M. (2009). T-duality as a duality of loop group bundles. Journal of Physics A: Mathematical and Theoretical (Print Edition), 42(16), 162001-1-162001-8.
2009 Brodzki, J., Varghese, M., Rosenberg, J., & Szabo, R. (2009). Non-commutative correspondences, duality and D-branes in bivariant K-theory. Advances in Theoretical and Mathematical Physics, 13(2), 497-552.
2008 Varghese, M., Melrose, R., & Singer, I. (2008). Equivariant and fractional index of projective elliptic operators. Journal of Differential Geometry, 78(3), 465-473.
2008 Brodzki, J., Varghese, M., Rosenberg, J., & Szabo, R. (2008). D-Branes, RR-Fields and Duality on Noncommutative Manifolds. Communications in Mathematical Physics, 277(3), 643-706.
2007 Varghese, M. (2007). T-Duality in type II string theory via noncommutative geometry and beyond. Progress of Theoretical Physics Supplement, 171(171), 237-257.
2007 Varghese, M., & Stevenson, D. (2007). Entire cyclic homology of stable continuous trace algebras. Bulletin of the London Mathematical Society, 39(1), 71-75.
2006 Carey, A., Hannabuss, K., & Varghese, M. (2006). Quantum Hall effect and noncommutative geometry. Journal of Geometry and Symmetry in Physics, 6(1), 16-36.
2006 Dodziuk, J., & Varghese, M. (2006). Kato's inequality and asymptotic spectral properties for discrete magnetic Laplacians. Contemporary Mathematics, 398, 69-82.
2006 Varghese, M. (2006). Heat kernels and the range of the trace on completions of twisted group algebras. Contemporary Mathematics, 398, 321-345.
2006 Varghese, M., Melrose, R., & Singer, I. (2006). Fractional analytic index. Journal of Differential Geometry, 74(2), 265-292.
2006 Varghese, M., & Rosenberg, J. (2006). T-duality for torus bundles with H-fluxes via noncommutative topology, II: the high-dimensional case and the T-duality group. Advances in Theoretical and Mathematical Physics, 10(1), 123-158.
2006 Bouwknegt, P., Evslin, J., Jurco, B., Varghese, M., & Sati, H. (2006). Flux compactifications on projective spaces and the S-duality puzzle. Advances in Theoretical and Mathematical Physics, 10(3), 345-394.
2006 Varghese, M., & Roberts, D. (2006). Yang-Mills theory for bundle gerbes. Journal of Physics A: Mathematical and Theoretical (Print Edition), 39(20), 6039-6044.
2006 Varghese, M., & Stevenson, D. (2006). On a generalised Connes-Hochschild-Kostant-Rosenberg theorem. Advances in Mathematics, 200(2), 303-335.
2006 Bouwknegt, P., Hannabuss, K., & Varghese, M. (2006). Nonassociative tori and applications to T-duality. Communications in Mathematical Physics, 264(1), 41-69.
2006 Dodziuk, J., Varghese, M., & Yates, S. (2006). Arithmetic properties of eigenvalues of generalized Harper operators on graphs. Communications in Mathematical Physics, 262(2), 269-297.
2005 Braverman, M., Carey, A., Farber, M., & Varghese, M. (2005). L2 torsion without the determinant class condition and extended L2 cohomology. Communications in Contemporary Mathematics, 7(4), 421-462.
2005 Kordyukov, Y., Varghese, M., & Shubin, M. (2005). Equivalence of spectral projections in semiclassical limit and a vanishing theorem for higher traces in K-theory. Journal fur die Reine und Angewandte Mathematik, 581(581), 193-236.
2005 Varghese, M., Melrose, R., & Singer, I. (2005). The index of projective families of elliptic operators. Geometry & Topology Online, 9(1), 341-373.
2005 Varghese, M., & Rosenberg, J. (2005). T-duality for torus bundles with H-fluxes via noncommutative topology. Communications in Mathematical Physics, 253(3), 705-721.
2005 Bouwknegt, P., Hannabuss, K., & Varghese, M. (2005). T-duality for principal torus bundles and dimensionally reduced Gysin sequences. Advances in Theoretical and Mathematical Physics, 9(5), 749-773.
2004 Bouwknegt, P., Evslin, J., & Varghese, M. (2004). T-duality: Topology change from H-flux. Communications in Mathematical Physics, 249(2), 383-415.
2004 Bouwknegt, P., Hannabuss, K., & Varghese, M. (2004). T-duality for principal torus bundles. The Journal of High Energy Physics, 3(18), WWW 1-WWW 10.
2004 Varghese, M., & Sati, H. (2004). Some relations between twisted K-theory and E8 gauge theory. The Journal of High Energy Physics, 3(3), WWW 1-WWW 22.
2004 Bouwknegt, P., Evslin, J., & Varghese, M. (2004). Topology and H-flux of T-dual manifolds. Physical Review Letters, 92(18), 181601-1-181601-3.
2003 Varghese, M., & Stevenson, D. (2003). Chern character in twisted K-theory: Equivariant and holomorphic cases. Communications in Mathematical Physics, 236(1), 161-186.
2003 Dodziuk, J., Linnell, P., Varghese, M., Schick, T., & Yates, S. (2003). Approximating L2 invariants and the Atiyah conjecture. Communications on Pure and Applied Mathematics, 56(7), 839-873.
2003 Varghese, M. (2003). The Novikov conjecture for low degree cohomology classes. Geometriae Dedicata, 99(1), 1-15.
2003 Varghese, M., Schick, T., & Yates, S. (2003). Approximating Spectral invariants of Harper operators on graphs II. Proceedings of the American Mathematical Society, 131(6), 1917-1923.
2003 Dodziuk, J., Linnell, P., Mathai, V., Schick, T., & Yates, S. (2003). Approximating L<sup>2</sup>-Invariants and the Atiyah Conjecture. Communications on Pure and Applied Mathematics, 56(7), 0839-0873.
2002 Varghese, M., & Shubin, M. (2002). Semiclassical asymptotics and gaps in the spectra of magnetic Schrödinger operators. Geometriae Dedicata, 91(1), 155-173.
2002 Varghese, M., & Yates, S. (2002). Approximating spectral invariants of Harper operators on graphs. Journal of Functional Analysis, 188(1), 111-136.
2001 Marcolli, M., & Varghese, M. (2001). Twisted index theory on good orbifolds, II: Fractional quantum numbers. Communications in Mathematical Physics, 217(1), 55-87.
2000 Bouwknegt, P., & Varghese, M. (2000). D-Branes, B-Fields and twisted K-theory. The Journal of High Energy Physics, 3(7), 1-11.
2000 Carey, A., Farber, M., & Varghese, M. (2000). Correspondences, von Neumann algebras and holomorphic L2 torsion. Canadian Journal of Mathematics-Journal Canadien de Mathematiques, 52(4), 695-736.
1999 Varghese, M., & Yates, S. (1999). Discrete Morse theory and extended L² homology. Journal of Functional Analysis, 168(1), 84-110.
1999 Varghese, M. (1999). K-theory of twisted group C*-algebras and positive scalar curvature. Contemporary Mathematics, 231, 203-225.
1999 Marcolli, M., & Mathai, V. (1999). Twisted index theory on good orbifolds, I: Noncommutative Bloch theory. Communications in Contemporary Mathematics, 1(4), 553-587.
1999 Carey, A., Hannabuss, K., & Mathai, V. (1999). Quantum Hall effect on the hyperbolic plane in the presence of disorder. Letters in Mathematical Physics, 47(3), 215-236.
1998 Carey, A., Hannabuss, K., Mathai, V., & McCann, P. (1998). Quantum hall effect on the hyperbolic plane. Communications in Mathematical Physics, 190(3), 629-673.
1998 Carey, A., Coulhon, T., Mathai, V., & Phillips, J. (1998). Von Neumann spectra near the spectral gap. Bulletin des Sciences Mathematiques, 122(3), 203-242.
1998 Varghese, M., & Rothenberg, M. (1998). On the homotopy invariance of L2 torsion for covering spaces. Proceedings of the American Mathematical Society, 126(3), 887-897.
1998 Varghese, M. (1998). Von Neumann algebra invariants of Dirac operators. Journal of Functional Analysis, 152(1), 1-21.
1998 Dodziuk, J., & Varghese, M. (1998). Approximating L2 invariants of amenable covering spaces: A combinatorial approach. Journal of Functional Analysis, 154(2), 359-378.
1997 Block, J., Mathai, V., & Weinberger, S. (1997). Homotopy invariance of novikov-shubin invariants and L<sup>2</sup> betti numbers. Proceedings of the American Mathematical Society, 125(12), 3757-3762.
1997 Mathai, V., & Wu, S. (1997). Equivariant holomorphic morse inequalities I: A heat kernel proof. Journal of Differential Geometry, 46(1), 78-98.
1997 Carey, A., Farber, M., & Mathai, V. (1997). Determinant lines, von Neumann algebras and L<sup>2</sup> torsion. Journal fur die Reine und Angewandte Mathematik, 484, 153-181.
1996 Mathai, V., & Shubin, M. (1996). Twisted L<sup>2</sup> invariants of non-simply connected manifolds and asymptotic L<sup>2</sup> Morse inequalities. Russian Journal of Mathematical Physics, 4(4), 499-526.
1996 Mathai, V. (1996). Inequalities for the novikov-shubin invariants. Proceedings of the American Mathematical Society, 124(8), 2585-2588.
1992 Mathai, V. (1992). Non-negative scalar curvature. Annals of Global Analysis and Geometry, 10(2), 103-123.
1992 Carey, A., & Mathai, V. (1992). L<sup>2</sup>-torsion invariants. Journal of Functional Analysis, 110(2), 377-409.
1992 Mathai, V. (1992). Spectral flow, eta invariants, and von Neumann algebras. Journal of Functional Analysis, 109(2), 442-456.
1992 Mathai, V. (1992). L<sup>2</sup>-analytic torsion. Journal of Functional Analysis, 107(2), 369-386.
1992 Mathai, V. (1992). Heat kernels and Thom forms. Journal of Functional Analysis, 104(1), 34-46.
1986 Mathai, V., & Quillen, D. (1986). Superconnections, thom classes, and equivariant differential forms. Topology, 25(1), 85-110.
— Han, F., & Mathai, V. (n.d.). Exotic Twisted Equivariant K-Theory.
— Hekmati, P., & Mathai, V. (n.d.). T-duality of current algebras and their quantization. Contemporary Mathematics, 584 (2012) 17-38.
— Mahanta, S., & Mathai, V. (n.d.). Operator algebra quantum groups of universal gauge groups.
— Hallam, M., & Mathai, V. (n.d.). Positive scalar curvature via end-periodic manifolds.
— Mathai, V. (n.d.). Verlinde modules and quantization.
— Mathai, V., & Singer, I. M. (n.d.). Twisted K-homology theory, twisted Ext-theory.
— Han, F., & Mathai, V. (n.d.). Witten Genus and Elliptic genera for proper actions.
— Mathai, V., & Wilkin, G. (n.d.). Fractional quantum numbers via complex orbifolds.
— Guo, H., Hochs, P., & Mathai, V. (n.d.). Equivariant Callias index theory via coarse geometry.
2006 Varghese, M. (2006). K-theory. In J. P. Francoise, G. L. Naber, & T. S. Tsun (Eds.), Encyclopedia of mathematical physics (pp. 246-254). Academic Press.
2006 Varghese, M., & Rosenberg, J. (2006). On mysteriously missing T-duals, H-flux and the T-duality Group. In M. Ge, & W. Zhang (Eds.), Differential geometry and physics (Vol. 10, pp. 350-358). 5 Toh Tuck Link, Singapore 596224: World Scientific Publishing.
2006 Marcolli, M., & Varghese, M. (2006). Towards the fractional quantum Hall effect: a noncummutative geometry perspective. In C. Consani, & M. Marcolli (Eds.), Noncommutative geometry and number theory (pp. 235-262). Germany: Springer.
1997 Varghese, M. (1997). L2 invariants of covering spaces. In Geometric analysis and lie theory in mathematics and physics, 1997 (pp. 209-242). Cambridge University Press.
2011 Varghese, M., & Wu, S. (2011). Analytic torsion of ℤ₂-graded elliptic complexes. In as published in Contemporary Mathematics Vol. 546 (pp. 199-212). Bonn, Germany: American Mathematical Society.
2010 Bouwknegt, P., Hannabuss, K., & Varghese, M. (2010). C*-algebras in tensor categories. In Motives, Quantum Field Theory, and Pseudodifferential Operators: Clay Mathematics Proceedings Vol 12 Vol. 12 (pp. 127-165). United States: American Mathematical Society.
2010 Hannabuss, K., & Varghese, M. (2010). Noncommutative principal torus bundles via parametrised strict deformation quantization. In American Mathematical Society. Proceedings of Symposia in Pure Mathematics Vol. 81 (pp. 133-147). United States: American Mathematical Society.
2008 Brodzki, J., Varghese, M., Rosenberg, J., & Szabo, R. (2008). D-branes, KK-theory and duality on noncommutative spaces. In International Conference on Non-commutative Geometry and Phsics; Journal of Physics: Conference Series, vol. 103 Vol. 103 (pp. 012004-1-012004-13). United Kingdom: Institute of Physics Publishing.
2006 Varghese, M., & Dodziuk, J. (2006). Kato’s inequality for magnetic Laplacians on graphs. In The ubiquitous heat kernel: AMS special session, the ubiquitous heat kernel, October 2-4, 2003, Boulder, Colorado (pp. 69-81). USA: American Mathematical Society.
2001 Varghese, M. (2001). On positivity of the Kadison constant and noncommutative Bloch theory. In Seiki Nishikawa (Ed.), Proceedings of the Fifth Pacific Rim Geometry Conference (pp. 107-124). Sendai, Japan: TOHOKU UNIVERSITY.
(jointly with P. Bouwknegt, Jan. 2015- Dec. 2017, $370K awarded).

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