Pure Mathematics

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Mathai Varghese

PhD (Massachusetts Institute of Technology)
Elder Professor of Mathematics, FAA FAustMS
Australian Laureate Fellow
2021 Hannan Medal and Lecture (AAS), Publicity
2021 George Szekeres Medal (AustMS), Publicity
2022 Professional Achievement Award, IIT (Chicago)
2025 Wallenberg guest Professor, Mittag-Leffler Institute
Director, Insititute for Geometry and its Applications
Editorial board, Journal of Topology and Analysis
Input for ERA 2023
Recent appointments & awards
Recent research interests
Recent preprints & publications
Recent ARC Grants & Postdocs
Major Conferences Co-organized
Students, Topics & Scholarships
Teaching, Administration
Contact details
JGP (IF= 1.6) virtual special issue
Index Theory, Duality and Related Fields
Plenary speaker at String Math 2023

Return to:- Pure Mathematics webpage, University of Adelaide

Selected recent publications
    2024

  1. Fei Han and V. Mathai, T-duality with H-flux for 2d sigma models, Communications in Mathematical Physics Volume 405, article number 294, (2024) 23 pp

    2. 2022

  2. Fei Han and V. Mathai, Witten Genus and Elliptic genera for proper actions Communications in Mathematical Physics 389, (2022) 1215-1239
  3. Fei Han and V. Mathai, T-duality, vertical holonomy line bundles and loop Hori formulae, Reviews in Mathematical Physics 34 no.7 (2022) 2250019, 25pp [2202.09908]
  4. H. Guo, and V. Mathai, Higher localised A-hat genera for proper actions and applications Journal of Functional Analysis 283 no. 12 (2022) 109695 59pp
  5. H. Guo, and V. Mathai, An equivariant Poincare duality for proper cocompact actions by matrix groups, Journal of Noncommutative Geometry 16 no. 4 (2022) 1397-1410

    6. 2021

  6. H. Guo, P. Hochs and V. Mathai, Coarse geometry and Callias quantisation, Transactions of the American Mathematical Society, 374 (2021), no. 4, 2479–2520.
  7. Jaklyn Crilly and V. Mathai, Exotic Courant algebroids and T-duality, Journal of Geometry and Physics, 163 (2021) 104155 12 pp.
  8. 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]
  9. 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]
  10. A. Linshaw and V. Mathai, T-duality and the exotic chiral de Rham complex, Communications in Mathematical Physics, 385 (2021) 1133–1161. [2008.00632]
  11. 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].
  12. 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]
  13. 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.. [1902.07391]
  14. 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 [2001.00322]

    15. 2020
  15. 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]
  16. 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]
  17. Fei Han and V. Mathai, Exotic Twisted Equivariant K-Theory, Journal of Geometry and Physics 158(2020) 103930 14pp [1712.06267]
  18. 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]
  19. V. Mathai, W. Zhang, F. Han, G. Yu (Editors), Index Theory, Duality and Related Fields, Special Issue of Journal of Geometry and Physics, (2020).

    20. 2019
  20. Fei Han and V. Mathai, Projective Elliptic genera and Elliptic Pseudodifferential genera, Advances in Mathematics 358, (2019), 106860 25 pp [1903.07035]
  21. V. Mathai and G. Wilkin, Fractional quantum numbers via complex orbifolds, Letters in Mathematical Physics 109, no. 11 (2019), 2473-2484 [1811.11748]
  22. 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]
  23. 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]
  24. G. Landi, V. Mathai, N. Higson, G. Yu (Editors), NCG 2017: Connes' 70th birthday celebration, Special Issue of Journal of Geometry and Physics, (2019).

    25. 2018
  25. M-T. Benameur, V.Mathai, Gap-labelling conjecture with non-zero magnetic field, Advances in Mathematics 325, (2018) 116-164, [1508.01064]
  26. 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]
  27. 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
  28. 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]
  29. 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]
  30. 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]
  31. 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.

    32. 2017
  32. 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]
  33. V. Mathai and G. C. Thiang, Differential topology of semimetals, Communications in Mathematical Physics, 355, no. 2,(2017) 561-602. Free access [1611.08961]
  34. 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
  35. P. Hochs and V. Mathai, Quantising proper actions on Spinc-manifolds, Asian Journal of Mathematics, 21 no. 4 (2017) 631-686, [1408.0085]

    36. 2016
  36. P. Hochs and V. Mathai, Spin manifolds and proper group actions, Advances in Mathematics, 292 (2016) 1-10, [1411.0781]
  37. K. Hannabuss, V. Mathai, G. C. Thiang, T-duality trivializes bulk-boundary correspondence: the parametrised case, Advances in Theoretical and Mathematical Physics, 20 no. 5 (2016) 1193-1226, [1510.04785]
  38. V. Mathai, G.C. Thiang, T-duality simplifies bulk-boundary correspondence: some higher dimensional cases, Annales Henri Poincare, 17 no. 12 (2016) 3399-3424, [1506.04492]
  39. P. Hochs, V. Mathai, Formal geometric quantisation for proper actions, Journal of Homotopy and Related Structures 11, no.3, (2016) 409-424, [1403.6542]
  40. V. Mathai and G. C. Thiang, T-duality simplifies bulk-boundary correspondence, Communications in Mathematical Physics, 345 no. 2, (2016) 675-701 Free access [1505.05250]

    41. 2015
  41. P. Hochs and V. Mathai, Geometric quantization and families of inner products, Advances in Mathematics, 282 (2015) 362-426, [1309.6760]
  42. M-T. Benameur and V. Mathai, Spectral sections, twisted rho invariants and positive scalar curvature J. Noncommutative Geometry, 9, no. 3, (2015) 821-850, [1309.5746]
  43. V. Mathai and Guo Chuan Thiang, T-duality and topological insulators, J. Physics A: Mathematical and Theoretical (Fast Track Communication), 48 (2015) no. 42, 42FT02, 10pp, [1503.01206]
    publicity at IOPSCIENCE
  44. A. Linshaw and V. Mathai, Twisted Chiral De Rham Complex, Generalized Geometry, and T-duality, Communications in Mathematical Physics, 339, No. 2, (2015) 663-697, [1412.0166]
  45. P.Bouwknegt, J.Evslin and V.Mathai, Spherical T-duality, Communications in Mathematical Physics, 337, No. 2, (2015) 909-954. [1405.5844]
  46. V.Mathai and H.Sati, Higher abelian gauge theory associated to gerbes on noncommutative deformed M5-branes and S-duality, J. Geometry and Physics 92 (2015) 240-251, [1404.2257]
  47. P.Bouwknegt, J.Evslin and V.Mathai, Spherical T-duality II: An infinity of spherical T-duals for non-principal SU(2)-bundles, J. Geometry and Physics, 92 (2015) 46-54, [1409.1296]
  48. F. Han, V. Mathai, Exotic twisted equivariant cohomology of loop spaces, twisted Bismut-Chern character and T-duality, Communications in Mathematical Physics, 337, No. 1, (2015) 127-150. [1405.1320]