Mathai Varghese

Professor Mathai Varghese

Elder Prof. Maths & Aust Laureate Fellow

School of Mathematical Sciences

Faculty of Engineering, Computer and Mathematical Sciences

Eligible to supervise Masters and PhD - email supervisor to discuss availability.


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 award of the Australian Mathematical Society medal in 2000, election as Fellow of the Australian Academy of Science in 2011, the award of the prestigious Australian Laureate Fellowship (2018-2022) and the prestigious 2021 Hannan medal which is a career award in mathematics from the Australian Academy of Science (see the twitter link below). Professor Varghese has published over 100 scientific articles in scholarly journals 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.

 

Video for the general public on my research.

My recent research interests include: index theory of projective families of elliptic operators; secondary invariants of elliptic operators; geometric quantization in the noncompact context; and noncommutative geometry. Recently my interests include topological obstructions to the existence of positive scalar curvature metrics on compact spin manifolds and projective index theory on loop spaces.

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 and 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.

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  • Journals

    Year Citation
    2021 MacDonald, L., Mathai, V., & Saratchandran, H. (2021). On the Chern character in Higher Twisted K-theory and spherical T-duality. Communications in Mathematical Physics, 385(1), 331-368.
    DOI
    2021 Guo, H., Hochs, P., & Varghese, M. (2021). Positive scalar curvature and an equivariant Callias-type index theorem for proper actions. Annals of K-Theory, 6(2), 319-356.
    DOI
    2021 Linshaw, A., & Varghese, M. (2021). T-duality and the exotic chiral de Rham complex. Communications in Mathematical Physics, 385(2), 1133-1161.
    DOI
    2021 Crilly, J., & Varghese, M. (2021). Exotic Courant algebroids and T-duality. Journal of Geometry and Physics, 163, 1-12.
    DOI Scopus2 WoS1
    2021 Han, F., Mathai, V., Yu, G., & Zhang, W. (2021). Foreword: VSI on Index Theory, Duality and Related Fields. Journal of Geometry and Physics, 163, 104156.
    DOI
    2021 Guo, H., & Varghese, M. (2021). An equivariant Poincaré duality for proper cocompact actions by matrix groups. Journal of Noncommutative Geometry, 13 pages.
    2021 Fok, C. -K., & Varghese, M. (2021). The ring structure of twisted equivariant KK-theory for noncompact Lie groups. Communications in Mathematical Physics, 385(2), 633-666.
    DOI
    2021 Varghese, M., & Wilkin, G. (2021). Fractional quantum numbers, complex orbifolds and noncommutative geometry. Journal of Physics A: Mathematical and Theoretical, 54(31), 314001-1-314001-18.
    DOI
    2021 Guo, H., Hochs, P., & Mathai, V. (2021). Equivariant Callias index theory via coarse geometry. Annales de l'Institut Fourier.
    2021 Guo, H., Hochs, P., & Mathai, V. (2021). Coarse geometry and Callias quantisation. Transactions of the American Mathematical Society, 374(4), 2479-2520.
    DOI Scopus1 WoS2
    2021 Han, F., & Mathai, V. (2021). T-duality, Jacobi forms and witten gerbe modules. Advances in Theoretical and Mathematical Physics.
    2020 Higson, N., Landi, G., Mathai, V., & Yu, G. (2020). Foreword. Journal of Geometry and Physics, 149, 103574.
    DOI
    2020 Varghese, M., & Rosenberg, J. (2020). The Riemann-Roch theorem on higher dimensional complex noncommutative tori. Journal of Geometry and Physics, 147, 103534-1-103534-9.
    DOI Scopus1 WoS1
    2020 Hallam, M., & Mathai, V. (2020). Positive scalar curvature via end-periodic manifolds. Annals of K-Theory, 5(3), 639-676.
    DOI
    2020 Han, F., & Varghese, M. (2020). Exotic twisted equivariant K-theory. Journal of Geometry and Physics, 158, 103930-1-103930-14.
    DOI
    2020 Benameur, M. T., & Mathai, V. (2020). Proof of the magnetic gap-labelling conjecture for principal solenoidal tori. Journal of Functional Analysis, 278(3), 9 pages.
    DOI Scopus1 WoS1
    2019 Guo, H., Varghese, M., & Wang, H. (2019). Positive scalar curvature and Poincaré duality for proper actions. Journal of Noncommutative Geometry, 13(4), 1381-1433.
    DOI WoS1
    2019 Mathai, V., Thiang, G. C., Hekmati, P., Bursztyn, H., Bouwknegt, P., & Baraglia, D. (2019). Foreword: String geometries, dualities and topological matter. Journal of Geometry and Physics, 138, 331-332.
    DOI
    2019 Mathai, V., & Thiang, G. C. (2019). Topological phases on the hyperbolic plane: fractional bulk-boundary
    correspondence. Advances in Theoretical and Mathematical Physics, 23(3), 803-840.

    DOI Scopus3 WoS3
    2019 Mathai, V., & Wilkin, G. (2019). Fractional quantum numbers via complex orbifolds. Letters in Mathematical Physics, 109(11), 2473-2484.
    DOI Scopus1 WoS1
    2019 Han, F., & Varghese, M. (2019). Projective elliptic genera and elliptic pseudodifferential genera. Advances in Mathematics, 358, 1-25.
    DOI Scopus1
    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.
    DOI Scopus1 WoS1
    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.
    DOI Scopus3 WoS3
    2018 Varghese, M., & Rosenberg, J. (2018). Group dualities, T-dualities, and twisted K-theory. Journal of the London Mathematical Society, 97(1), 1-23.
    DOI Scopus2 WoS2
    2018 Linshaw, A., & Mathai, V. (2018). T-duality of singular spacetime compactifications in an H-flux. Journal of Geometry and Physics, 129, 269-278.
    DOI Scopus2 WoS2
    2018 Benameur, M., & Varghese, M. (2018). Gap-labelling conjecture with nonzero magnetic field. Advances in Mathematics, 325, 116-164.
    DOI Scopus4 WoS4
    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.
    DOI Scopus8 WoS8
    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.
    DOI Scopus17 WoS19
    2017 Mathai, V., & Melrose, R. (2017). Geometry of pseudodifferential algebra bundles and fourier integral operators. Duke Mathematical Journal, 166(10), 1859-1922.
    DOI Scopus1 WoS1
    2017 Varghese, M., & Thiang, G. (2017). Differential topology of semimetals. Communications in Mathematical Physics, 355(2), 561-602.
    DOI Scopus18 WoS18
    2017 Hochs, P., & Mathai, V. (2017). Quantising proper actions on SpinC-manifolds. Asian Journal of Mathematics, 21(4), 631-686.
    DOI Scopus10 WoS12
    2016 Mathai, V., & Thiang, G. (2016). T-Duality simplifies bulk–boundary correspondence: some higher dimensional cases. Annales Henri Poincare, 17(12), 3399-3424.
    DOI Scopus10 WoS10
    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.
    DOI Scopus6 WoS6
    2016 Mathai, V., & Thiang, G. (2016). T-Duality simplifies bulk-boundary correspondence. Communications in Mathematical Physics, 345(2), 675-701.
    DOI Scopus18 WoS16
    2016 Hochs, P., & Varghese, M. (2016). Formal geometric quantisation for proper actions. Journal of Homotopy and Related Structures, 11(3), 409-424.
    DOI Scopus1 WoS1
    2016 Hochs, P., & Mathai, V. (2016). Spin-structures and proper group actions. Advances in Mathematics, 292, 1-10.
    DOI Scopus3 WoS5
    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.
    DOI Scopus7 WoS8
    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.
    DOI Scopus5 WoS5
    2015 Varghese, M., & Thiang, G. (2015). T-duality of topological insulators. Journal of Physics A: Mathematical and Theoretical, 48(42), 42FT02-1-42FT02-10.
    DOI Scopus12 WoS13
    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.
    DOI Scopus2 WoS2
    2015 Bouwknegt, P., Evslin, J., & Mathai, V. (2015). Spherical T-duality. Communications in Mathematical Physics, 337(2), 909-954.
    DOI Scopus6 WoS6
    2015 Linshaw, A., & Varghese, M. (2015). Twisted chiral de Rham complex, generalized geometry, and T-duality. Communications in Mathematical Physics, 339(2), 663-697.
    DOI Scopus5 WoS6
    2015 Benameur, M., & Mathai, V. (2015). Spectral sections, twisted rho invariants and positive scalar curvature. Journal of Noncommutative Geometry, 9(3), 821-850.
    DOI Scopus3 WoS3
    2015 Hochs, P., & Mathai, V. (2015). Geometric quantization and families of inner products. Advances in Mathematics, 282, 362-426.
    DOI Scopus16 WoS17
    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.
    DOI Scopus4 WoS4
    2014 Benameur, M. T., & 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.
    DOI Scopus1 WoS4
    2014 Mathai, V., & Rosenberg, J. (2014). T-duality for circle bundles via noncommutative geometry. Advances in Theoretical and Mathematical Physics, 18(6), 1437-1462.
    DOI Scopus4 WoS3
    2013 Dey, R., & Varghese, M. (2013). Holomorphic Quillen determinant line bundles on integral compact Kähler manifolds. Quarterly Journal of Mathematics, 64(3), 785-794.
    DOI Scopus4 WoS4
    2013 Bernameur, M., & Varghese, M. (2013). Conformal invariants of twisted Dirac operators and positive scalar curvature. Journal of Geometry and Physics, 70, 39-47.
    DOI Scopus5 WoS3
    2012 Hekmati, P., & Varghese, M. (2012). T-duality of current algebras and their quantization. Contemporary Mathematics, 584, 17-37.
    DOI WoS5
    2012 Varghese, M., & Wu, S. (2012). Topology and Flux of T-Dual Manifolds with Circle Actions. Communications in Mathematical Physics, 316(1), 279-286.
    DOI Scopus6 WoS5
    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.
    DOI Scopus2 WoS1
    2012 Bouwknegt, P., Varghese, M., & Wu, S. (2012). Bundle gerbes and moduli spaces. Journal of Geometry and Physics, 62(1), 1-10.
    DOI Scopus2 WoS2
    2011 Varghese, M., & Wu, S. (2011). Analytic torsion for twisted de Rham complexes. Journal of Differential Geometry, 88(2), 297-332.
    DOI Scopus15 WoS16
    2011 Mahanta, S., & Varghese, M. (2011). Operator algebra quantum homogeneous spaces of universal gauge groups. Letters in Mathematical Physics, 97(3), 263-277.
    DOI Scopus3 WoS3
    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.
    DOI Scopus9 WoS8
    2011 Varghese, M., & Rosenberg, J. (2011). A noncommutative sigma-model. Journal of Noncommutative Geometry, 5(2), 265-294.
    DOI Scopus11 WoS10
    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.
    Europe PMC5
    2010 Mathai, V., Melrose, R., & Singer, I. (2010). The index of projective families of elliptic operators: The decomposable case. Asterisque, 328, 1-35.
    Scopus7
    2010 Varghese, M., & Zhang, W. (2010). Geometric quantization for proper actions. Advances in Mathematics, 225(3), 1224-1247.
    DOI Scopus23 WoS25
    2010 Varghese, M., & Wu, S. (2010). Twisted analytic torsion. Science China Mathematics, 53(3), 555-563.
    DOI Scopus8 WoS8
    2009 Varghese, M., Melrose, R., & Singer, I. (2009). The index of projective families of elliptic operators: the decomposable case. Asterisque, 328(328), 255-296.
    WoS14
    2009 Chakraborty, P., & Varghese, M. (2009). The geometry of determinant line bundles in noncommutative geometry. Journal of Noncommutative Geometry, 3(4), 559-578.
    DOI Scopus4 WoS4
    2009 Green, R., & Varghese, M. (2009). Harmonic Cheeger-Simons characters with applications. Journal of Geometry and Physics, 59(5), 663-672.
    DOI Scopus4 WoS4
    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.
    DOI Scopus6 WoS6
    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.
    DOI Scopus16 WoS13
    2008 Varghese, M., Melrose, R., & Singer, I. (2008). Equivariant and fractional index of projective elliptic operators. Journal of Differential Geometry, 78(3), 465-473.
    DOI Scopus9 WoS8
    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.
    DOI Scopus31 WoS34
    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.
    DOI
    2007 Varghese, M., & Stevenson, D. (2007). Entire cyclic homology of stable continuous trace algebras. Bulletin of the London Mathematical Society, 39(1), 71-75.
    DOI Scopus4 WoS4
    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.
    DOI Scopus6
    2006 Dodziuk, J., & Varghese, M. (2006). Kato's inequality and asymptotic spectral properties for discrete magnetic Laplacians. Contemporary Mathematics, 398, 69-82.
    WoS37
    2006 Varghese, M. (2006). Heat kernels and the range of the trace on completions of twisted group algebras. Contemporary Mathematics, 398, 321-345.
    WoS12
    2006 Varghese, M., Melrose, R., & Singer, I. (2006). Fractional analytic index. Journal of Differential Geometry, 74(2), 265-292.
    DOI Scopus21 WoS21
    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.
    DOI Scopus41 WoS51
    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.
    DOI Scopus7 WoS9
    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.
    DOI Scopus2 WoS2
    2006 Varghese, M., & Stevenson, D. (2006). On a generalised Connes-Hochschild-Kostant-Rosenberg theorem. Advances in Mathematics, 200(2), 303-335.
    DOI Scopus15 WoS18
    2006 Bouwknegt, P., Hannabuss, K., & Varghese, M. (2006). Nonassociative tori and applications to T-duality. Communications in Mathematical Physics, 264(1), 41-69.
    DOI Scopus85 WoS80
    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.
    DOI
    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.
    DOI Scopus8 WoS8
    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.
    DOI Scopus5 WoS8
    2005 Varghese, M., Melrose, R., & Singer, I. (2005). The index of projective families of elliptic operators. Geometry & Topology Online, 9(1), 341-373.
    DOI Scopus26 WoS26
    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.
    DOI Scopus97 WoS100
    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.
    DOI Scopus30 WoS31
    2004 Bouwknegt, P., Evslin, J., & Varghese, M. (2004). T-duality: Topology change from H-flux. Communications in Mathematical Physics, 249(2), 383-415.
    DOI Scopus146 WoS167
    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.
    DOI Scopus34 WoS28
    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.
    DOI Scopus31 WoS18
    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.
    DOI Scopus67 WoS65
    2003 Varghese, M., Murray, M., & Stevenson, D. (2003). Type-1 D-branes in an H-flux and twisted KO-theory. The Journal of High Energy Physics, 11(11), www 1-www 22.
    DOI Scopus5 WoS10
    2003 Varghese, M., & Stevenson, D. (2003). Chern character in twisted K-theory: Equivariant and holomorphic cases. Communications in Mathematical Physics, 236(1), 161-186.
    DOI Scopus30 WoS35
    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.
    DOI WoS64
    2003 Varghese, M. (2003). The Novikov conjecture for low degree cohomology classes. Geometriae Dedicata, 99(1), 1-15.
    DOI Scopus12 WoS15
    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.
    DOI Scopus13 WoS14
    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.
    Scopus56
    2002 Varghese, M., & Shubin, M. (2002). Semiclassical asymptotics and gaps in the spectra of magnetic Schrödinger operators. Geometriae Dedicata, 91(1), 155-173.
    DOI Scopus7
    2002 Bouwknegt, P., Carey, A., Varghese, M., Murray, M., & Stevenson, D. (2002). Twisted K-theory and K-theory of bundle gerbes. Communications in Mathematical Physics, 228(1), 17-45.
    DOI Scopus127 WoS132
    2002 Varghese, M., & Yates, S. (2002). Approximating spectral invariants of Harper operators on graphs. Journal of Functional Analysis, 188(1), 111-136.
    DOI Scopus25 WoS27
    2001 Marcolli, M., & Varghese, M. (2001). Twisted index theory on good orbifolds, II: Fractional quantum numbers. Communications in Mathematical Physics, 217(1), 55-87.
    DOI Scopus26 WoS24
    2000 Bouwknegt, P., & Varghese, M. (2000). D-Branes, B-Fields and twisted K-theory. The Journal of High Energy Physics, 3(7), 1-11.
    DOI Scopus89 WoS110
    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.
    DOI Scopus3 WoS5
    1999 Varghese, M., & Yates, S. (1999). Discrete Morse theory and extended L² homology. Journal of Functional Analysis, 168(1), 84-110.
    DOI Scopus3 WoS3
    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.
    DOI Scopus29 WoS29
    1999 Carey, A., Hannabus, K., & Mathai, V. (1999). Quantum Hall effect on the hyperbolic plane in the presence of disorder. Letters in Mathematical Physics, 47(3), 215-236.
    DOI Scopus15 WoS16
    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.
    DOI Scopus4 WoS4
    1998 Varghese, M. (1998). Von Neumann algebra invariants of Dirac operators. Journal of Functional Analysis, 152(1), 1-21.
    DOI Scopus3 WoS3
    1998 Dodziuk, J., & Varghese, M. (1998). Approximating L2 invariants of amenable covering spaces: A combinatorial approach. Journal of Functional Analysis, 154(2), 359-378.
    DOI Scopus24 WoS23
    1998 Carey, A. L., Hannabuss, K. C., Mathai, V., & McCann, P. (1998). Quantum hall effect on the hyperbolic plane. Communications in Mathematical Physics, 190(3), 629-673.
    DOI Scopus54 WoS52
    1998 Carey, A. L., Coulhon, T., Mathai, V., & Phillips, J. (1998). Von Neumann spectra near the spectral gap. Bulletin des Sciences Mathematiques, 122(3), 203-242.
    DOI Scopus2 WoS2
    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.
    Scopus25 WoS20
    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.
    DOI Scopus2 WoS2
    1997 Mathai, V., & Wu, S. (1997). Equivariant holomorphic morse inequalities I: A heat kernel proof. Journal of Differential Geometry, 46(1), 78-98.
    DOI Scopus9 WoS9
    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.
    Scopus4 WoS5
    1996 Mathai, V. (1996). Inequalities for the novikov-shubin invariants. Proceedings of the American Mathematical Society, 124(8), 2585-2588.
    DOI
    1992 Mathai, V. (1992). Non-negative scalar curvature. Annals of Global Analysis and Geometry, 10(2), 103-123.
    DOI Scopus6
    1992 Mathai, V. (1992). Spectral flow, eta invariants, and von Neumann algebras. Journal of Functional Analysis, 109(2), 442-456.
    DOI Scopus23 WoS22
    1992 Mathai, V. (1992). L<sup>2</sup>-analytic torsion. Journal of Functional Analysis, 107(2), 369-386.
    DOI Scopus39 WoS37
    1992 Mathai, V. (1992). Heat kernels and Thom forms. Journal of Functional Analysis, 104(1), 34-46.
    DOI Scopus3 WoS3
    1992 Carey, A. L., & Mathai, V. (1992). L<sup>2</sup>-torsion invariants. Journal of Functional Analysis, 110(2), 377-409.
    DOI Scopus24 WoS25
    1986 Mathai, V., & Quillen, D. (1986). Superconnections, thom classes, and equivariant differential forms. Topology, 25(1), 85-110.
    DOI Scopus246 WoS250
    Marcolli, M., & Mathai, V. (n.d.). Twisted higher index theory on good orbifolds and fractional quantum
    numbers.
    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.
  • Book Chapters

    Year Citation
    2006 Varghese, M. (2006). K-theory. In J. Francoise, G. Naber, & T. Tsun (Eds.), Encyclopedia of mathematical physics (pp. 246-254). Academic Press.
    DOI
    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.
    DOI Scopus13 WoS14
    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.
  • Conference Papers

    Year Citation
    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.
    DOI WoS9
    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.
    DOI WoS13
    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.
    DOI Scopus1 WoS1
    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.

Current Discovery Project grants:

Advances in Index Theory, Australian Laureate Fellowship
(Mar. 2018 - Mar. 2023, $1.64 million + $500K awarded)

Coarse Geometry: a novel approach to the Callias index & topological matter
(jointly with P. Hochs and G. C. Thiang,, Jan. 2020- Dec. 2022, $507K awarded)

Differential Topology
Honours and MPhil level course, 
University of Adelaide, 
Taught in 2016, 2017.

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  • Current Higher Degree by Research Supervision (University of Adelaide)

    Date Role Research Topic Program Degree Type Student Load Student Name
    2021 Principal Supervisor Index Theory and Geometric Analysis Doctor of Philosophy Doctorate Full Time Miss Elizabeth Marilyn Auke Jagersma
    2020 Co-Supervisor Invariants of Families of 4-Manifolds Master of Philosophy Master Full Time Mr Joshua Celeste
    2020 Principal Supervisor Further Developments of Geometric Methods motivated by Condensed Matter Physics Doctor of Philosophy Doctorate Full Time Ms Marisa Christin Schult
  • Past Higher Degree by Research Supervision (University of Adelaide)

    Date Role Research Topic Program Degree Type Student Load Student Name
    2018 - 2020 Principal Supervisor Higher twisted K-theory Master of Philosophy Master Full Time Mr David Leonard Brook
    2017 - 2018 Principal Supervisor Hitchin's Projectively Flat Connection and the Moduli Space of Higgs Bundles Master of Philosophy Master Full Time Mr John Benjamin McCarthy
    2017 - 2019 Principal Supervisor Analytic Pontryagin Duality Doctor of Philosophy Doctorate Full Time Mr Johnny Khai Yang Lim
    2017 - 2019 Principal Supervisor Geometric K-homology and the Atiyah-Singer index theorem Master of Philosophy Master Full Time Mr Samuel Mills
    2016 - 2018 Principal Supervisor Positive Scalar Curvature and Callias-Type Index Theorems for Proper Actions Doctor of Philosophy Doctorate Full Time Mr Hao Guo
    2016 - 2018 Principal Supervisor Generalised Eta Invariants, End-Periodic Manifolds, and their Applications to Positive Scalar Curvature Master of Philosophy Master Full Time Mr Michael Hallam
    2015 - 2018 Principal Supervisor Metrics and Special Kähler Geometry on the Moduli Spaces of Higgs Bundles and Hitchin Systems Doctor of Philosophy Doctorate Full Time Mr Zhenxi Huang
    2012 - 2014 Principal Supervisor Noncommutative Geometry Methods In Number Theory Master of Philosophy Master Full Time Mr Konrad Karol Pilch
    2009 - 2012 Principal Supervisor Twisted Analytic Torsion Master of Science in Mathematical and Computer Sciences Master Full Time Mr Ryan Mickler
    2007 - 2011 Principal Supervisor Higher Tannaka Duality Doctor of Philosophy under a Cotutelle Agreement with Doctorate Full Time Mr James Wallbridge
    2006 - 2009 Co-Supervisor Loop Groups, Higgs Fields and Generalised String Classes Doctor of Philosophy Doctorate Full Time Dr Raymond Vozzo
    2006 - 2011 Principal Supervisor A Fourier-Mukai Transform for Invariant Differential Cohomology Doctor of Philosophy Doctorate Full Time Mr Richard Green
    2005 - 2008 Principal Supervisor Regularized Equivariant Euler Classes and Gamma Functions Doctor of Philosophy Doctorate Full Time Mr Rongmin Lu
    2005 - 2010 Co-Supervisor Fundamental Bigroupoids and 2-Covering Spaces Doctor of Philosophy Doctorate Part Time Dr David Roberts
    1999 - 2002 Principal Supervisor Properties and applications of the vector Harper operator Doctor of Philosophy Doctorate Full Time Dr Sam Yates
  • Other Supervision Activities

    Date Role Research Topic Location Program Supervision Type Student Load Student Name
    2006 - 2006 Co-Supervisor Generalized Geometry University of Adelaide School of Mathematical Sciences (Pure Mathematics) Master Full Time David Baraglia
    2003 - 2004 Principal Supervisor K-theory and a twisted analogue University of Adelaide School of Mathematical Science (Pure Mathematics) Master Full Time Rongmin Lu
    1994 - 1998 Principal Supervisor Discrete Morse theory and L2 homology University of Adelaide Department of Pure Mathematics Master Part Time Stuart Yates
    1994 - 1997 Principal Supervisor Spectral properties of the Laplacian on p-forms on the Heisenberg group Department of Pure Mathematics, University of Adelaide Pure Mathematics Doctorate Full Time Luke Schubert
  • Position: Elder Prof. Maths & Aust Laureate Fellow
  • Phone: 83134173
  • Email: mathai.varghese@adelaide.edu.au
  • Fax: 8313 3696
  • Campus: North Terrace
  • Building: Ingkarni Wardli, floor 7
  • Room: 7 31
  • Org Unit: Mathematical Sciences

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