Professor Mathai Varghese

ARC Australian Laureate Fellow

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 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
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 Guest 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.

My Research
Career
Publications
Grants and Funding
Teaching
Supervision
Professional Activities
Contact

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.

Appointments

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

Awards and Achievements

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	-

Education

Date Institution name Country Title

1986 Massachusetts Institute of Technology United States PhD (Pure Mathematics)

1981 Illinois Institute of Technology United States BA (Mathematics)
Postgraduate Training

Date Title Institution Country

1981 - 1986 PhD in Mathematics Massachusetts Institute of Technology United States
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

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

Journals

Year	Citation
2024	Han, F., & Mathai, V. (2024). T-duality with $H$-flux for $2d$ $σ$-models. Communications in Mathematical Physics, 405(12), 23pp. DOI
2023	Mathai, V., & Melrose, R. B. (2023). Index and small bundle gerbes.
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. DOI
2022	Guo, H., & Mathai, V. (2022). Higher localised Â genera for proper actions and applications. Journal of Functional Analysis, 283(12), 59 pages. DOI
2022	Han, F., & Mathai, V. (2022). Witten Genus and Elliptic genera for proper actions. Communications in Mathematical Physics, 389(2), 1215-1239. DOI
2021	Guo, H., Hochs, P., & Mathai, V. (2021). Equivariant Callias index theory via coarse geometry. Annales de l'Institut Fourier, 71(6), 2387-2430. DOI WoS2
2021	Guo, H., Hochs, P., & Mathai, V. (2021). Coarse geometry and Callias quantisation. Transactions of the American Mathematical Society, 374(4), 2479-2520. DOI Scopus3 WoS4
2021	Han, F., & Mathai, V. (2021). T-duality, Jacobi forms and Witten gerbe modules. Advances in Theoretical and Mathematical Physics, 25(5), 1235-1266. DOI Scopus2
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 Scopus1
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 Scopus1 WoS1
2021	Crilly, J., & Varghese, M. (2021). Exotic Courant algebroids and T-duality. Journal of Geometry and Physics, 163, 104155-1-104155-12. DOI Scopus3 WoS2
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, 16(4), 1397-1410. DOI
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
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 Scopus3 WoS3
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 Scopus6 WoS3
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 Scopus7 WoS6
2019	Mathai, V., & Wilkin, G. (2019). Fractional quantum numbers via complex orbifolds. Letters in Mathematical Physics, 109(11), 2473-2484. DOI Scopus1 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 Scopus7 WoS5
2019	Han, F., & Varghese, M. (2019). Projective elliptic genera and elliptic pseudodifferential genera. Advances in Mathematics, 358, 106860-1-106860-25. DOI Scopus3 WoS1
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. DOI Scopus5 WoS3
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 Scopus5 WoS5
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 Scopus5 WoS4
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 Scopus4 WoS3
2018	Benameur, M., & Varghese, M. (2018). Gap-labelling conjecture with nonzero magnetic field. Advances in Mathematics, 325, 116-164. DOI Scopus7 WoS6
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 Scopus10 WoS9
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 Scopus22 WoS22
2017	Mathai, V., & Melrose, R. (2017). Geometry of pseudodifferential algebra bundles and fourier integral operators. Duke Mathematical Journal, 166(10), 1859-1922. DOI Scopus2 WoS1
2017	Varghese, M., & Thiang, G. (2017). Differential topology of semimetals. Communications in Mathematical Physics, 355(2), 561-602. DOI Scopus29 WoS24
2017	Hochs, P., & Mathai, V. (2017). Quantising proper actions on SpinC-manifolds. Asian Journal of Mathematics, 21(4), 631-686. DOI Scopus15 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 Scopus12 WoS12
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 Scopus7 WoS7
2016	Mathai, V., & Thiang, G. (2016). T-Duality simplifies bulk-boundary correspondence. Communications in Mathematical Physics, 345(2), 675-701. DOI Scopus25 WoS19
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 Scopus7 WoS7
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 Scopus12 WoS11
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 Scopus6 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 Scopus17 WoS15
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 Scopus5 WoS3
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 Scopus8 WoS9
2015	Benameur, M., & Mathai, V. (2015). Spectral sections, twisted rho invariants and positive scalar curvature. Journal of Noncommutative Geometry, 9(3), 821-850. DOI Scopus4 WoS4
2015	Hochs, P., & Mathai, V. (2015). Geometric quantization and families of inner products. Advances in Mathematics, 282, 362-426. DOI Scopus19 WoS20
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 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. 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 WoS6
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 Scopus7 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 Scopus17 WoS17
2011	Mahanta, S., & Varghese, M. (2011). Operator algebra quantum homogeneous spaces of universal gauge groups. Letters in Mathematical Physics, 97(3), 263-277. DOI Scopus4 WoS4
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 Scopus13 WoS12
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 PMC7
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. Scopus9
2010	Varghese, M., & Zhang, W. (2010). Geometric quantization for proper actions. Advances in Mathematics, 225(3), 1224-1247. DOI Scopus28 WoS29
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. WoS15
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 Scopus10 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 Scopus34 WoS35
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 Scopus10 WoS11
2006	Dodziuk, J., & Varghese, M. (2006). Kato's inequality and asymptotic spectral properties for discrete magnetic Laplacians. Contemporary Mathematics, 398, 69-82. WoS42
2006	Varghese, M. (2006). Heat kernels and the range of the trace on completions of twisted group algebras. Contemporary Mathematics, 398, 321-345. WoS13
2006	Varghese, M., Melrose, R., & Singer, I. (2006). Fractional analytic index. Journal of Differential Geometry, 74(2), 265-292. DOI Scopus23 WoS22
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 Scopus46 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. DOI Scopus9 WoS11
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 Scopus3 WoS3
2006	Varghese, M., & Stevenson, D. (2006). On a generalised Connes-Hochschild-Kostant-Rosenberg theorem. Advances in Mathematics, 200(2), 303-335. DOI Scopus17 WoS19
2006	Bouwknegt, P., Hannabuss, K., & Varghese, M. (2006). Nonassociative tori and applications to T-duality. Communications in Mathematical Physics, 264(1), 41-69. DOI Scopus91 WoS83
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 Scopus1
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 Scopus11 WoS9
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 Scopus7 WoS9
2005	Varghese, M., Melrose, R., & Singer, I. (2005). The index of projective families of elliptic operators. Geometry & Topology Online, 9(1), 341-373. DOI Scopus29 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 Scopus107 WoS104
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 Scopus35 WoS33
2004	Bouwknegt, P., Evslin, J., & Varghese, M. (2004). T-duality: Topology change from H-flux. Communications in Mathematical Physics, 249(2), 383-415. DOI Scopus180 WoS182
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 Scopus47 WoS33
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 Scopus44 WoS21
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 Scopus79 WoS73
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 Scopus9 WoS9
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 Scopus36 WoS37
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 WoS69
2003	Varghese, M. (2003). The Novikov conjecture for low degree cohomology classes. Geometriae Dedicata, 99(1), 1-15. DOI Scopus16 WoS16
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. Scopus69
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 Scopus143 WoS138
2002	Varghese, M., & Yates, S. (2002). Approximating spectral invariants of Harper operators on graphs. Journal of Functional Analysis, 188(1), 111-136. DOI Scopus27 WoS28
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 Scopus35 WoS25
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 Scopus104 WoS113
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
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. DOI Scopus38 WoS32
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 Scopus17 WoS17
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.
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 Scopus27 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 Scopus64 WoS54
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 L<sup>2</sup> torsion. Journal fur die Reine und Angewandte Mathematik, 484, 153-181. Scopus28 WoS21
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
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 Scopus24 WoS24
1992	Mathai, V. (1992). L<sup>2</sup>-analytic torsion. Journal of Functional Analysis, 107(2), 369-386. DOI Scopus48 WoS39
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 Scopus29 WoS26
1986	Mathai, V., & Quillen, D. (1986). Superconnections, thom classes, and equivariant differential forms. Topology, 25(1), 85-110. DOI Scopus281 WoS268

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 Scopus19 WoS16
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.
2006	Mathai, V. (2006). K-Theory. In Encyclopedia of Mathematical Physics: Five-Volume Set (pp. V3-246-V3-254). DOI
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 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, $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.

Current Higher Degree by Research Supervision (University of Adelaide)

Date	Role	Research Topic	Program	Degree Type	Student Load	Student Name
2023	Principal Supervisor	K-Theory of Topological Insulators	Doctor of Philosophy	Doctorate	Full Time	Mr Joshua Celeste
2022	Co-Supervisor	Families Seiberg-Witten Invariants of 4-Manifold Families.	Doctor of Philosophy	Doctorate	Full Time	Mr Joshua Rikihana John Tomlin

Past Higher Degree by Research Supervision (University of Adelaide)

Date	Role	Research Topic	Program	Degree Type	Student Load	Student Name
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

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

Committee Memberships

Date	Role	Committee	Institution	Country
2024 - 2024	Chair	2024 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

Editorial Boards

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

Offices Held

Date Office Name Institution Country

2006 - 2009 Vice President in charge of annual conferences Australian Mathematical Society Australia

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

Position: ARC Australian Laureate Fellow
Phone: 83134173
Email: mathai.varghese@adelaide.edu.au
Fax: 83133696
Campus: North Terrace
Building: Ingkarni Wardli, floor 7
Org Unit: Mathematical Sciences

Professor Mathai Varghese

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Awards and Achievements

Education

Postgraduate Training

Research Interests

Journals

Book Chapters

Conference Papers

Current Higher Degree by Research Supervision (University of Adelaide)

Past Higher Degree by Research Supervision (University of Adelaide)

Other Supervision Activities

Committee Memberships

Editorial Boards

Offices Held

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