• Fellow, Australian Academy of Science, elected in 2011 to a learned academy.
  
• ARC Australian Laureate Fellow (2018-2023), category 1 research fellowship.
  
• 2021 Hannan Medal and Lecture from the Australian Academy of Science
  
• 2021 George Szekeres Medal from the Australian Mathematical Society
  

Research Income (2019-2021; for ERA 2023)

• DP200100729; Coarse Geometry: a novel approach to the Callias index & topological matter (jointly with PIs P. Hochs and G. C. Thiang,, July 2020- July 2023, $507K awarded) $253.5K in 2019-2021.
• DP170101054; Parametrised gauge theory and positive scalar curvature, (jointly with D. Baraglia, July 2017- Jun 2020, $335K awarded) $167.5K in 2019-2021.
• FL170100020; Advances in Index Theory and Applications (March 2018-March 2023, $1.64 million + .5 million awarded) $1,284K in 2019-2021.
• Total research income in 2019-2023 > $1.7 million.

Research output (2016-2021; for ERA 2023)

2021

1. H. Guo, P. Hochs and V. Mathai, Coarse geometry and Callias quantisation, Transactions of the American Mathematical Society, 374 (2021), no. 4, 2479–2520.
2. Jaklyn Crilly and V. Mathai, Exotic Courant algebroids and T-duality, Journal of Geometry and Physics, 163 (2021) 104155 12 pp.
3. L. MacDonald, V. Mathai, H. Saratchandran, On the Chern character in Higher Twisted K-theory and spherical T-duality, Communications in Mathematical Physics 385 (2021) 331-368. [2007.02507]
4. Chi-Kwong Fok and V. Mathai, The ring structure of twisted equivariant KK-theory for noncompact Lie groups, Communications in Mathematical Physics, 385 (2021) 633-666. [1903.05298]
5. A. Linshaw and V. Mathai, T-duality and the exotic chiral de Rham complex, Communications in Mathematical Physics, 385 (2021) 1133–1161. [2008.00632]
6. V. Mathai and G. Wilkin, Fractional Quantum Numbers, Complex Orbifolds and Noncommutative Geometry, Journal of Physics A: Mathematical and Theoretical Special issue, Noncommutative Geometry in Physics, 54 (2021) 314001, 18pp [2004.06666].
7. H. Guo, P. Hochs and V. Mathai, Positive scalar curvature and an equivariant Callias-type index theorem for proper actions, Annals of K-theory, 6 no.2 (2021) 319–356. [2001.07336]
8. H. Guo, P. Hochs and V. Mathai, Equivariant Callias index theory via coarse geometry, Annales de l’institut Fourier, 71 (2021) no. 6, 2387-2430..
9. Fei Han and V. Mathai, T-Duality, Jacobi Forms and Witten Gerbe Modules, Advances in Theoretical and Mathematical Physics, 25 no. 5 (2021) 1235 – 1266.

2020

10. M. T. Benameur and V. Mathai, Proof of the magnetic gap-labelling conjecture for principal solenoidal tori, Journal of Functional Analysis 278 (2020) 108323, 8 pp, [1806.06302]
11. M. Hallam and V. Mathai, Positive scalar curvature metrics via end-periodic manifolds, Annals of K-theory 5 no. 3 (2020) 639-676. [1706.09354]
12. Fei Han and V. Mathai, Exotic Twisted Equivariant K-Theory, Journal of Geometry and Physics 158(2020) 103930 14pp [1712.06267]
13. V. Mathai and J. Rosenberg, The Riemann-Roch theorem on higher dimensional complex noncommutative tori, Journal of Geometry and Physics 147 (2020) 103534, 9 pp, [1907.10200]
14. V. Mathai, W. Zhang, F. Han, G. Yu (Editors), Index Theory, Duality and Related Fields, Special Issue of Journal of Geometry and Physics, (2020).

2019

15. Fei Han and V. Mathai, Projective Elliptic genera and Elliptic Pseudodifferential genera, Advances in Mathematics 358, (2019), 106860 25 pp [1903.07035]
16. V. Mathai and G. Wilkin, Fractional quantum numbers via complex orbifolds, Letters in Mathematical Physics 109, no. 11 (2019), 2473-2484 [1811.11748]
17. Hao Guo, V. Mathai and Hang Wang, Positive scalar curvature and Poincaré duality for proper actions, Journal of Noncommutative Geometry 13 no.4 (2019) 1381-1433. [1609.01404]
18. V. Mathai and G. C. Thiang, Topological phases on the hyperbolic plane: fractional bulk-boundary correspondence, Advances in Theoretical and Mathematical Physics, 23 no. 3 (2019) 803-840, [1712.02952]
19. G. Landi, V. Mathai, N. Higson, G. Yu (Editors), NCG 2017: Connes' 70th birthday celebration, Special Issue of Journal of Geometry and Physics, (2019).

2018

20. M-T. Benameur, V.Mathai, Gap-labelling conjecture with non-zero magnetic field, Advances in Mathematics 325, (2018) 116-164, [1508.01064]
21. A. Linshaw and V. Mathai, T-duality of singular spacetime compactifications in an H-flux, Journal of Geometry and Physics, 129, no. 7 (2018) 269-278, Free Access [1710.09927]
22. V. Mathai and J. Rosenberg, Group dualities, T-dualities, and twisted K-theory, Journal of the London Mathematical Society, 97, no. 1 (2018) 1-23, Free Access [1603.00969]
    JLMS certificate
23. K. Hannabuss, V. Mathai, G. C. Thiang, T-duality simplifies bulk-boundary correspondence: the noncommutative case, Letters in Mathematical Physics, 108, no. 5 (2018) 1163-1201, [1603.00116]
24. Fei Han and V. Mathai, T-duality in an H-flux: exchange of momentum and winding, Communications in Mathematical Physics, 363, no. 1 (2018) 333-350. Free access [1710.07274]
25. P.Bouwknegt, J.Evslin and V. Mathai, Spherical T-duality and the spherical Fourier-Mukai transform, Journal of Geometry and Physics, 133 (2018), 303-314, [1502.04444]
26. V. Mathai, G. Thiang, P. Hekmati, H. Bursztyn, P. Bouwknegt, D. Baraglia, (Editors) String geometries, Dualities and Topological Matter, Special Issue of Journal of Geometry and Physics, 132 (2018) 306 pp.

2017

27. V. Mathai and R.B. Melrose, Geometry of Pseudodifferential algebra bundles and Fourier Integral Operators, Duke Mathematical Journal, 166 no.10 (2017) 1859-1922, [1210.0990]
28. V. Mathai and G. C. Thiang, Differential topology of semimetals, Communications in Mathematical Physics, 355, no. 2,(2017) 561-602. Free access [1611.08961]
29. V. Mathai and G. C. Thiang, Global topology of Weyl semimetals and Fermi arcs, Journal of Physics A: Mathematical and Theoretical (Letter) 50 no. 11 (2017) 11LT01, 11pp Free Access [1607.02242]
    publicity at JPhys+, Highlights Certificate
30. P. Hochs and V. Mathai, Quantising proper actions on Spin^c-manifolds, Asian Journal of Mathematics, 21 no. 4 (2017) 631-686, [1408.0085]

2016

31. T-duality simplifies bulk-boundary correspondence: some higher dimensional cases (with G.C. Thiang), Annales Henri Poincare, 17 no. 12 (2016) 3399–3424, [1506.04492]
32. T-duality trivializes bulk-boundary correspondence: the parametrised case (with K. Hannabuss and G. C. Thiang), Advances in Theoretical and Mathematical Physics, 20 no. 5 (2016) 1193-1226, [1510.04785]
33. Formal geometric quantisation for proper actions (with P. Hochs), Journal of Homotopy and Related Structures, 11, no.3, (2016) 409-424, [1403.6542] >
34. T-duality simplifies bulk-boundary correspondence (with Guo Chuan Thiang), Communications in Mathematical Physics, 345 no. 2, (2016) 675-701 [1505.05250]
35. Spin manifolds and proper group actions, (with P. Hochs), Advances in Mathematics, 292 (2016) 1-10, [1411.0781]