Mathai Varghese

Research Interests

Algebraic and Differential Geometry Conformal Field Theory Field Theory and String Theory K Theory Mathematical Aspects of Condensed Matter Mathematical Aspects of Quantum Mathematical Physics Operator Algebras and Functional Analysis Partial Differential Equations Pure Mathematics Quantum Gravity and String Theory Quantum Physics Topology

Professor Mathai Varghese

Aust Laureate Fellow & Elder Prof of Maths

School of Computer and Mathematical Sciences

Faculty of Sciences, Engineering and Technology

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

Professor Mathai Varghese is renowned 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 Sir Thomas Elder Chair in Mathematics in 2013. The quality of Professor Varghese’s research has been recognised with awards over the years (see below) including
 1) award of the 2000 Australian Mathematical Society medal, https://austms.org.au/awards-grants/awards/the-australian-mathematical-society-medal/
2) election as Fellow of the Australian Academy of Science in 2011, https://www.science.org.au/profile/mathai-varghese
3) the award of the prestigious Australian Laureate Fellowship (2018-2022),http://www.arc.gov.au/2017-laureate-profile-professor-mathai-varghese
4) award of the 2021 Hannan medal and Lecture from the Australian Academy of Science,https://www.science.org.au/supporting-science/awards-and-opportunities/hannan-medal
5) award of the 2021 George Szekeres medal from the Australian Mathematical Society.https://austms.org.au/awards-grants/awards/the-george-szekeres-medal/
6) presented the 2022 Professional Achievement Award, Illinois Institute of Technology (Chicago).https://www.iit.edu/alumniawards/2022-award-winners
7) award of 2025 Wallenberg Visiting Professor at the Mittag-Leffler Institute in Stockholm, Sweden.
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.

Date Position Institution name
2018 - 2022 Australian Laureate Fellow University of Adelaide
2013 - ongoing Sir Thomas Elder Professor of Mathematics University of Adelaide
2009 - ongoing Director of the Institute for Geometry and its Applications (IGA) University of Adelaide
2007 - ongoing Adjunct Professor of Mathematics Australian National University

Date Type Title Institution Name Country Amount
2025 Honour Wallenberg guest Professorship Mittag-Leffler Institute, Stockholm Sweden -
2022 Award Professional Achievement Award Illinois Institute of Technology United States -
2021 Award George Szekeres medal Australian Mathematical Society Australia -
2021 Research Award Hannan medal and Lecture Australian Academy of Science Australia -
2018 Fellowship Australian Laureate Fellowship University of Adelaide Australia $1.64 million
2013 Award Discovery Outstanding Researcher Award University of Adelaide Australia $630,000
2013 Fellowship Fellow of the Royal Society of South Australia Royal Society of South Australia Australia -
2011 Fellowship Fellow of the Australian Academy of Science, FAA Australian Academy of Science Australia -
2007 Fellowship Australian Professorial Fellowship University of Adelaide Australia $500,000
2006 Fellowship Senior Research Fellowship Erwin Schrodinger Institute for Mathematical Physics Austria -
2001 Fellowship ARC Senior Research Fellowship University of Adelaide Australia -
2000 Award Medal, Australian Mathematical Society Australian Mathematical Society Australia -
2000 Fellowship Fellow, Australian MathematicalSociety, FAustMS AustralianMathematicalSociety Australia -
2000 Fellowship Clay Mathematics Institute Research Fellowship Massachusetts Institute of Technology United States -
1994 Fellowship Australian Research Fellowship University of Adelaide Australia -

Date Institution name Country Title
1986 Massachusetts Institute of Technology United States PhD (Pure Mathematics)
1981 Illinois Institute of Technology United States BA (Mathematics)

Date Title Institution Country
1981 - 1986 PhD in Mathematics Massachusetts Institute of Technology United States

Year Citation
2025 Han, F., & Mathai, V. (2025). Loop Hori Formulae for T-duality and Twisted Bismut-Chern Character.
2025 Mathai, V., & Melrose, R. B. (2025). Index and small bundle gerbes. Advances in Mathematics, 483, 110679.
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2024 Han, F., & Mathai, V. (2024). T-duality with H-Flux for 2d σ-Models. Communications in Mathematical Physics, 405(12), 294-1-294-23.
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2022 Guo, H., & Mathai, V. (2022). Higher localised  genera for proper actions and applications. Journal of Functional Analysis, 283(12), 59 pages.
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2022 Han, F., & Mathai, V. (2022). T-duality, vertical holonomy line bundles and loop Hori formulae. Reviews in Mathematical Physics, 34(7), 2250019-1-2250019-25.
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2022 Varghese, M., & Guo, H. (2022). An equivariant Poincaré duality for proper cocompact actions by matrix groups. Journal of Noncommutative Geometry, 16(4), 1397-1410.
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2022 Han, F., & Mathai, V. (2022). Witten Genus and Elliptic genera for proper actions. Communications in Mathematical Physics, 389(2), 1215-1239.
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2021 Guo, H., Hochs, P., & Mathai, V. (2021). Equivariant Callias index theory via coarse geometry. Annales de l'Institut Fourier, 71(6), 2387-2430.
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2021 Guo, H., Hochs, P., & Mathai, V. (2021). Coarse geometry and Callias quantisation. Transactions of the American Mathematical Society, 374(4), 2479-2520.
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2021 Han, F., & Mathai, V. (2021). T-duality, Jacobi forms and Witten gerbe modules. Advances in Theoretical and Mathematical Physics, 25(5), 1235-1266.
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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.
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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.
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2021 Linshaw, A., & Varghese, M. (2021). T-duality and the exotic chiral de Rham complex. Communications in Mathematical Physics, 385(2), 1133-1161.
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2021 Crilly, J., & Varghese, M. (2021). Exotic Courant algebroids and T-duality. Journal of Geometry and Physics, 163, 104155-1-104155-12.
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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.
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2021 Guo, H., & Varghese, M. (2021). An equivariant Poincaré duality for proper cocompact actions by matrix groups. Journal of Noncommutative Geometry, 16(4), 1397-1410.
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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.
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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.
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2020 Higson, N., Landi, G., Mathai, V., & Yu, G. (2020). Foreword. Journal of Geometry and Physics, 149, 103574.
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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.
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2020 Hallam, M., & Mathai, V. (2020). Positive scalar curvature via end-periodic manifolds. Annals of K-Theory, 5(3), 639-676.
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2020 Han, F., & Varghese, M. (2020). Exotic twisted equivariant K-theory. Journal of Geometry and Physics, 158, 103930-1-103930-14.
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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.
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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.
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2019 Mathai, V., & Wilkin, G. (2019). Fractional quantum numbers via complex orbifolds. Letters in Mathematical Physics, 109(11), 2473-2484.
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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.
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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.
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2019 Han, F., & Varghese, M. (2019). Projective elliptic genera and elliptic pseudodifferential genera. Advances in Mathematics, 358, 106860-1-106860-25.
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2019 Guo, H., Hochs, P., & Varghese, M. (2019). Positive scalar curvature and callias-type index theorems for proper actions. Bulletin of the Australian Mathematical Society, 99(2), 342-343.
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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.
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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.
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2018 Varghese, M., & Rosenberg, J. (2018). Group dualities, T-dualities, and twisted K-theory. Journal of the London Mathematical Society, 97(1), 1-23.
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2018 Linshaw, A., & Mathai, V. (2018). T-duality of singular spacetime compactifications in an H-flux. Journal of Geometry and Physics, 129, 269-278.
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2018 Benameur, M., & Varghese, M. (2018). Gap-labelling conjecture with nonzero magnetic field. Advances in Mathematics, 325, 116-164.
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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.
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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.
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2017 Mathai, V., & Melrose, R. (2017). Geometry of pseudodifferential algebra bundles and fourier integral operators. Duke Mathematical Journal, 166(10), 1859-1922.
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2017 Varghese, M., & Thiang, G. (2017). Differential topology of semimetals. Communications in Mathematical Physics, 355(2), 561-602.
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2017 Hochs, P., & Mathai, V. (2017). Quantising proper actions on SpinC-manifolds. Asian Journal of Mathematics, 21(4), 631-686.
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2016 Mathai, V., & Thiang, G. (2016). T-Duality simplifies bulk–boundary correspondence: some higher dimensional cases. Annales Henri Poincare, 17(12), 3399-3424.
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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.
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2016 Mathai, V., & Thiang, G. (2016). T-Duality simplifies bulk-boundary correspondence. Communications in Mathematical Physics, 345(2), 675-701.
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2016 Hochs, P., & Varghese, M. (2016). Formal geometric quantisation for proper actions. Journal of Homotopy and Related Structures, 11(3), 409-424.
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2016 Hochs, P., & Mathai, V. (2016). Spin-structures and proper group actions. Advances in Mathematics, 292, 1-10.
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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.
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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.
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2015 Varghese, M., & Thiang, G. (2015). T-duality of topological insulators. Journal of Physics A: Mathematical and Theoretical, 48(42), 42FT02-1-42FT02-10.
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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.
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2015 Bouwknegt, P., Evslin, J., & Mathai, V. (2015). Spherical T-duality. Communications in Mathematical Physics, 337(2), 909-954.
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2015 Linshaw, A., & Varghese, M. (2015). Twisted chiral de Rham complex, generalized geometry, and T-duality. Communications in Mathematical Physics, 339(2), 663-697.
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2015 Benameur, M., & Mathai, V. (2015). Spectral sections, twisted rho invariants and positive scalar curvature. Journal of Noncommutative Geometry, 9(3), 821-850.
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2015 Hochs, P., & Mathai, V. (2015). Geometric quantization and families of inner products. Advances in Mathematics, 282, 362-426.
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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.
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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.
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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 Scopus5 WoS4
2013 Dey, R., & Varghese, M. (2013). Holomorphic Quillen determinant line bundles on integral compact Kähler manifolds. Quarterly Journal of Mathematics, 64(3), 785-794.
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2013 Bernameur, M., & Varghese, M. (2013). Conformal invariants of twisted Dirac operators and positive scalar curvature. Journal of Geometry and Physics, 70, 39-47.
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2012 Hekmati, P., & Varghese, M. (2012). T-duality of current algebras and their quantization. Contemporary Mathematics, 584, 17-37.
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2012 Varghese, M., & Wu, S. (2012). Topology and Flux of T-Dual Manifolds with Circle Actions. Communications in Mathematical Physics, 316(1), 279-286.
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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.
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2012 Bouwknegt, P., Varghese, M., & Wu, S. (2012). Bundle gerbes and moduli spaces. Journal of Geometry and Physics, 62(1), 1-10.
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2011 Varghese, M., & Wu, S. (2011). Analytic torsion for twisted de Rham complexes. Journal of Differential Geometry, 88(2), 297-332.
DOI Scopus18 WoS18
2011 Mahanta, S., & Varghese, M. (2011). Operator algebra quantum homogeneous spaces of universal gauge groups. Letters in Mathematical Physics, 97(3), 263-277.
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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.
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2011 Asghari, A. (2011). Psychometric Properties of a Modified version of the Roland-Morris Disability Questionnaries (M-RMDQ). ARCHIVES OF IRANIAN MEDICINE, 14(5), 327-331.
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2011 Mathai, V. (2011). Verlinde modules and quantization.
2010 Mathai, V., Melrose, R., & Singer, I. (2010). The index of projective families of elliptic operators: The decomposable case. Asterisque, 328, 1-35.
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2010 Varghese, M., & Zhang, W. (2010). Geometric quantization for proper actions. Advances in Mathematics, 225(3), 1224-1247.
DOI Scopus30 WoS31
2010 Varghese, M., & Wu, S. (2010). Twisted analytic torsion. Science China Mathematics, 53(3), 555-563.
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2009 Varghese, M., Melrose, R., & Singer, I. (2009). The index of projective families of elliptic operators: the decomposable case. Asterisque, 328(328), 255-296.
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2009 Chakraborty, P., & Varghese, M. (2009). The geometry of determinant line bundles in noncommutative geometry. Journal of Noncommutative Geometry, 3(4), 559-578.
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2009 Green, R., & Varghese, M. (2009). Harmonic Cheeger-Simons characters with applications. Journal of Geometry and Physics, 59(5), 663-672.
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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.
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2008 Varghese, M., Melrose, R., & Singer, I. (2008). Equivariant and fractional index of projective elliptic operators. Journal of Differential Geometry, 78(3), 465-473.
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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 Scopus35 WoS36
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.
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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 Scopus10 WoS12
2006 Dodziuk, J., & Varghese, M. (2006). Kato's inequality and asymptotic spectral properties for discrete magnetic Laplacians. Contemporary Mathematics, 398, 69-82.
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2006 Varghese, M. (2006). Heat kernels and the range of the trace on completions of twisted group algebras. Contemporary Mathematics, 398, 321-345.
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2006 Varghese, M., Melrose, R., & Singer, I. (2006). Fractional analytic index. Journal of Differential Geometry, 74(2), 265-292.
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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 Scopus47 WoS52
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.
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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.
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2006 Varghese, M., & Stevenson, D. (2006). On a generalised Connes-Hochschild-Kostant-Rosenberg theorem. Advances in Mathematics, 200(2), 303-335.
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2006 Bouwknegt, P., Hannabuss, K., & Varghese, M. (2006). Nonassociative tori and applications to T-duality. Communications in Mathematical Physics, 264(1), 41-69.
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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.
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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.
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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.
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2005 Varghese, M., Melrose, R., & Singer, I. (2005). The index of projective families of elliptic operators. Geometry & Topology Online, 9(1), 341-373.
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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.
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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.
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2004 Bouwknegt, P., Evslin, J., & Varghese, M. (2004). T-duality: Topology change from H-flux. Communications in Mathematical Physics, 249(2), 383-415.
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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.
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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 Scopus46 WoS22
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.
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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.
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2003 Varghese, M., & Stevenson, D. (2003). Chern character in twisted K-theory: Equivariant and holomorphic cases. Communications in Mathematical Physics, 236(1), 161-186.
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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.
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2003 Varghese, M. (2003). The Novikov conjecture for low degree cohomology classes. Geometriae Dedicata, 99(1), 1-15.
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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.
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2003 Dodziuk, J., Linnell, P., Mathai, V., Schick, T., & Yates, S. (2003). Approximating L2-Invariants and the Atiyah Conjecture. Communications on Pure and Applied Mathematics, 56(7), 0839-0873.
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2002 Mathai, X., & Shubin, M. (2002). Semiclassical asymptotics and gaps in the spectra of magnetic Schrodinger operators. GEOMETRIAE DEDICATA, 91(1), 155-173.
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2002 Varghese, M., & Shubin, M. (2002). Semiclassical asymptotics and gaps in the spectra of magnetic Schrödinger operators. Geometriae Dedicata, 91(1), 155-173.
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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.
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2002 Varghese, M., & Yates, S. (2002). Approximating spectral invariants of Harper operators on graphs. Journal of Functional Analysis, 188(1), 111-136.
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2001 Marcolli, M., & Varghese, M. (2001). Twisted index theory on good orbifolds, II: Fractional quantum numbers. Communications in Mathematical Physics, 217(1), 55-87.
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2000 Bouwknegt, P., & Varghese, M. (2000). D-Branes, B-Fields and twisted K-theory. The Journal of High Energy Physics, 3(7), 1-11.
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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.
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2000 Mathai, V., & Singer, I. M. (2000). Twisted K-homology theory, twisted Ext-theory.
1999 Marcolli, M., & Mathai, V. (1999). Twisted index theory on good orbifolds, I: Noncommutative Bloch theory. Communications in Contemporary Mathematics, 1(4), 553-587.
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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.
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1999 Varghese, M., & Yates, S. (1999). Discrete Morse theory and extended L² homology. Journal of Functional Analysis, 168(1), 84-110.
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1999 Varghese, M. (1999). K-theory of twisted group C*-algebras and positive scalar curvature. Contemporary Mathematics, 231, 203-225.
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.
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1998 Varghese, M. (1998). Von Neumann algebra invariants of Dirac operators. Journal of Functional Analysis, 152(1), 1-21.
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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 Scopus27 WoS25
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 Scopus65 WoS59
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
1998 Marcolli, M., & Mathai, V. (1998). Twisted higher index theory on good orbifolds and fractional quantum
numbers.
1997 Mathai, V., & Wu, S. (1997). Equivariant holomorphic morse inequalities I: A heat kernel proof. Journal of Differential Geometry, 46(1), 78-98.
DOI Scopus10 WoS10
1997 Carey, A., Farber, M., & Mathai, V. (1997). Determinant lines, von Neumann algebras and L2 torsion. Journal Fur Die Reine Und Angewandte Mathematik, 484, 153-181.
Scopus29 WoS24
1997 Block, J., Mathai, V., & Weinberger, S. (1997). Homotopy invariance of novikov-shubin invariants and L2 betti numbers. Proceedings of the American Mathematical Society, 125(12), 3757-3762.
DOI Scopus2 WoS2
1996 Mathai, V., & Shubin, M. (1996). Twisted L2 invariants of non-simply connected manifolds and asymptotic L2 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 Scopus26 WoS24
1992 Mathai, V. (1992). L2-analytic torsion. Journal of Functional Analysis, 107(2), 369-386.
DOI Scopus50 WoS46
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). L2-torsion invariants. Journal of Functional Analysis, 110(2), 377-409.
DOI Scopus30 WoS29
1986 Mathai, V., & Quillen, D. (1986). Superconnections, thom classes, and equivariant differential forms. Topology, 25(1), 85-110.
DOI Scopus288 WoS284

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 WoS10
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 WoS14
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, extended to Dec 2025; $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,  extended to Dec 2025; $507K awarded)

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

Date Role Research Topic Program Degree Type Student Load Student Name
2022 - 2025 Co-Supervisor A Connected Sum Formula for the Seiberg-Witten Invariant of 4-Manifold Families Doctor of Philosophy Doctorate Full Time Mr Joshua Rikihana John Tomlin
2020 - 2022 Co-Supervisor The families Seiberg-Witten invariants of smooth families of Kahler surfaces Master of Philosophy Master Full Time Mr Joshua Celeste
2018 - 2020 Principal Supervisor Higher twisted K-theory Master of Philosophy Master Full Time Mr David Leonard Brook
2017 - 2019 Principal Supervisor Analytic Pontryagin Duality Doctor of Philosophy Doctorate Full Time Mr Johnny Khai Yang Lim
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 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

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

Date Role Committee Institution Country
2025 - 2028 Member Pawsey Medal committee Australian Academy of Science Australia
2023 - 2025 Chair George Szekeres Medal committee Australian Mathematical Society Australia
2015 - 2018 Member Sectional Committee 1: Mathematical Sciences Australian Academy of Science Australia
2015 - 2017 Member Elizabeth And Frederick White Research Conferences Awards Committee Australian Academy of Science Australia
2011 - 2012 Chair Gavin Brown Prize committee Australian Mathematical Society Australia
2007 - 2009 Chair Mahler Lecturer committee Australian Mathematical Society Australia
2006 - 2009 Vice-President Steering committee Australian Mathematical Society Australia
2006 - 2009 Vice-President AustMS conferences program committee Australian Mathematical Society Australia

Date Role Editorial Board Name Institution Country
2018 - 2019 Editor-In-chief Journal of Geometry and Physics Elsevier Netherlands
2017 - 2018 Editor-In-chief Journal of Geometry and Physics Elsevier Netherlands
2016 - ongoing Editor Letters in Journal of Geometry and Physics Elsevier Netherlands
2014 - ongoing Editor Journal of Geometry and Physics Elsevier Netherlands
2010 - 2011 Editor Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics Cambridge University Press, Cambridge, UK. Australia
2010 - 2014 Board Member Advisory Board Australian Mathematical Society Australia
2008 - 2016 Editor Proceedings of the American Mathematical Society American Mathematical Society, Providence, Rhode Island United States

Date Office Name Institution Country
2006 - 2009 Vice President in charge of annual conferences Australian Mathematical Society Australia

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