Professor Mathai Varghese

Elder Professor of Mathematics
Professor Mathai Varghese
  Org Unit Mathematical Sciences
  Email mathai.varghese@adelaide.edu.au
  Telephone +61 8 8313 4173
  Location Floor/Room 7 31 ,  Ingkarni Wardli Building ,   North Terrace

Professor Mathai Varghese is the Director of the Institute for Geometry and its Applications (IGA). He is also the Elder Professor of Mathematics within the School of Mathematical Sciences at the University of Adelaide, Australian Laureate Fellow, as well as an Adjunct Professor of Mathematics within the Mathematical Sciences Institute at the Australian National University.

Mathai was elected fellow of the Australian Academy of Science (2011), fellow of the Australian Mathematical Society (2000) and fellow of the Royal Society of South Australia (2013).

Mathai was awarded the Australian Mathematical Society Medal in 2000.

Mathai's input for ERA 2015

3-year Research job opportunity: apply online now!

Editorial activities:

2016 - current, Editor, Letters of Journal of Geometry and Physics,

2014 - current, Editor, Journal of Geometry and Physics, Elsevier, Netherlands. (ERA Journal Ranking = A)

2017-18, Managing Guest Editor, JGP special issue on Noncommutative Geometry 2017: a celebration of Alain Connes 70th birthday

2016-17, Managing Guest Editor, JGP special issue on String geometries, Dualities and Topological Matter: Call for papers

2011, Guest Editor for two special issues, no. 1 and no. 2, volume 90, 2011, Journal of the Australian Mathematical Society, Cambridge University Press, Cambridge, UK. (ERA Journal Ranking = B)

2008 - 2016, Editor in charge of the section, Global Analysis, Noncommutative Geometry, and the Mathematics of String Theory, Proceedings of the American Mathematical Society, Providence, Rhode Island, USA. (ERA Journal Ranking = A)

  • Ph.D. Doctor of Philosophy     (Massachusetts Institute of Technology)
  • B.A. Bachelor of Arts              (Illinois Institute of Technology)
  • I.C.S.E. High School Certificate   (Bishop Cotton Boys' School, Bangalore)

  • 2017, Australian Laureate Fellowship
  • 2016, Herbert Howe Lecture series, Department of Mathematics, University of Denver, Denver, Colorado (May 17-20).
    See this link for a report on the public lecture
    , or the AAS newsletter item.
  • 2016-2018,  Member, Sectional Committee 1: Mathematical Sciences, Australian Academy of Science.
    Further information on election of candidates to the Australian Academy of Science can be found here. 
  • 2015-2017,  Member,  Elizabeth and Frederick White Research Awards Committee, 
    Australian Academy of Science.  Further information on the award can be found here. 
  • 2013-current, Sir Thomas Elder Chair, full Professor (level E), University of Adelaide, Adelaide. ,
  • 2013-2015, awarded ARC Discovery Outstanding Researcher Award. ,
  • 2011, elected Fellow, Australian Academy of Science;

  • 2011-2012, Chair/outgoing Chair, selection committee for the Gavin Brown Prize of the AustMS;

  • 2009 - current, Director, Institute for Geometry and its Applications, University of Adelaide, Adelaide;
  • 2009, Chair, selection committee for the Mahler Lecturer.
  • 2007-2011, awarded ARC Professorial Fellowship. ,
  • 2006-2009, Vice President (portfolio: annual conferences), Australian Mathematical Society;
  • 2007, Member, selection committee for the AustMS medal.
  • 2006, (spring semester) Senior Research Fellow, Erwin Schrödinger Institute, Vienna.
  • 2006 - current, Personal Chair, full Professor (level E), University of Adelaide, Adelaide.
  • 2001 - 2005, ARC Senior Research Fellow (level D) University of Adelaide, Adelaide.
  • 2000 - 2001, Clay Mathematics Institute Research Fellow and
    Visiting Scientist, Massachusetts Institute of Technology, Cambridge, Massachusetts.
  • 2000, awarded Australian Mathematical Society Medal.
  •  

    Geometric analysis, mathematical physics, noncommutative geometry, mathematics of string theory, mathematics of quantum theory, topological insulators.

  • 2014, String theory and contemporary culture: Vibrating strings, similar to the vibrations of violin strings, give rise to fundamental particles such as quarks and gluons, which in turn are the constituents of protons, neutrons, and electrons etc., establishing a close connection between music and string theory. Since science drives our economy, changing our culture by creating a popular awareness and understanding of science is an important goal of ours. An example is the recent consultancy role of Bouwknegt and myself on a production of the Australian Dance Theatre entitled Multiverse, where the main choreographer, Garry Stewart, has used duality in string theory to generate ideas for a wonderful dance piece on both artistic and intellectual levels. Multiverse premiered at the Space Theatre, Adelaide Festival Centre on 10 July 2014 and we were invited guests.
  • Detailed Research Interests

    ARC Discovery Project grants (current) :

    Parametrised gauge theory and positive scalar curvature,
    (jointly with D. Baraglia, Jan. 2017- Dec. 2019, $335K awarded)

    Ubiquity of K-theory and T-duality
    (jointly with P. Bouwknegt, Jan. 2015- Dec. 2017, $370K awarded).

    All recent ARC Discovery Project grants and Postdoc supervision

    Mathai has co-authored over 100 refereed publications.

    Selected recent publications

  • 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]
  • V. Mathai and G. C. Thiang, Differential topology of semimetals, Communications in Mathematical Physics, (published online) 48 pages. [1611.08961]
  • 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 [1607.02242]
    publicity at JPhys+
  • P. Hochs, V. Mathai, Quantising proper actions on Spinc-manifolds, Asian Journal of Mathematics, (to appear), 62 pages, [1408.0085]
  • K. Hannabuss, V. Mathai, G. C. Thiang, T-duality simplifies bulk-boundary correspondence: the parametrised case, Advances in Theoretical and Mathematical Physics, 20 no. 5 (2016) 1193-1226, [1510.04785]
  • P. Hochs, V. Mathai, Formal geometric quantisation for proper actions, Journal of Homotopy and Related Structures, 11, no.3, (2016) 409-424, [1403.6542]
  • 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]
  • V. Mathai and G. C. Thiang, T-duality simplifies bulk-boundary correspondence, Communications in Mathematical Physics, 345 no. 2, (2016) 675-701 [1505.05250]
  • P. Hochs and V. Mathai, Spin manifolds and proper group actions, Advances in Mathematics, 292 (2016) 1-10, [1411.0781]
  • M-T. Benameur and V. Mathai, Spectral sections, twisted rho invariants and positive scalar curvature,  Journal of Noncommutative Geometry, 9, no. 3, (2015) 821-850, [1309.5746]
  • V. Mathai and G.C. Thiang, T-duality and topological insulators, Journal of Physics A: Mathematical and Theoretical (Fast Track Communication) 48 (2015) 42FT02 (10pp), [1503.01206]
    publicity at IOPSCIENCE
  • P. Hochs and V. Mathai, Geometric quantization and families of inner products, Advances in Mathematics, 282 (2015) 362-426, [1309.6760]
  • 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]
  • P.Bouwknegt, J.Evslin and V.Mathai, Spherical T-duality, Communications in Mathematical Physics, 337, No. 2, (2015) 909-954. [1405.5844]
  • V.Mathai and H.Sati, Higher abelian gauge theory associated to gerbes on noncommutative deformed M5-branes and S-duality, Journal of Geometry and Physics, 92 (2015) 240-251, [1404.2257]
  • 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]
  • 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]
  • V. Mathai, J. Rosenberg, T-duality for circle bundles via noncommutative geometry, Advances in Theoretical and Mathematical Physics, 18, no. 6 (2014) 1437-1462, [1306.4198]
  • M-T. Benameur, V. Mathai, Index type invariants for twisted signature complexes and homotopy invariance, Mathematical Proceedings of the Cambridge Philosophical Society, 156 no.3 (2014) 473-503, [1202.0272]
  • R. Dey, V. Mathai, Holomorphic Quillen determinant line bundles on integral compact Kahler manifolds, The Quarterly J. of Mathematics, Quillen memorial issue, 64 (2013), 785-794, [1202.5213]
  • M-T. Benameur, V. Mathai, Conformal invariants of twisted Dirac operators and positive scalar curvature J. Geometry and Physics, 70 (2013) 39-47, [1210.0301] Erratum, J. Geometry and Physics, 76 (2014) 263-264.
  • V. Mathai and S. Wu, Topology and Flux of T-Dual Manifolds with Circle Actions, Communications in Mathematical Physics, 316 (2012) 279-286. [1108.5045]
  • P. Bouwknegt, V. Mathai and S. Wu, Bundle gerbes and moduli spaces, J. Geometry and Physics,, 62 no.1, (2012) 1-10, [1107.3687]
  • V. Mathai and S.Wu, Analytic torsion for twisted de Rham complexes, J. Differential Geometry, 88 (2011) 297-332, [0810.4204]
  • V. Mathai and J. Rosenberg, A noncommutative sigma-model, J. Noncommutative Geometry, 5 no 2 (2011) 265-294, [0903.4241]
  • V. Mathai, W. Zhang, Geometric quantization for proper actions, Advances in Mathematics, 225 no.3 (2010) 1224--1247 [0806.3138v2]
  • P. Bouwknegt, K. Hannabuss, V. Mathai, C*-algebras in tensor categories, Clay Mathematics Proceedings, 12 (2010) 127-165. [math.QA/0702802]
  • V. Mathai, R.B. Melrose, I.M. Singer, The index of projective families of elliptic operators: the decomposable case, Asterisque, 328 (2009) 255-296, [0809.0028]
  • P. Chakraborty, V. Mathai, The geometry of determinant line bundles in noncommutative geometry, J. Noncommutative Geometry, 3 no.4 (2009) 559-578. [0804.3232v2]
  • J. Brodzki, V. Mathai, J. Rosenberg, R. Szabo, Noncommutative correspondences, duality and D-branes in bivariant K-theory, Advances in Theoretical and Mathematical Physics, 13 no. 2 (2009) 497-552. [0708.2648]
  • V. Mathai, R.B. Melrose and I.M. Singer, Equivariant and fractional index of projective elliptic operators, J. Differential Geometry, 78 no.3 (2008) 465-473. [math.DG/0611819]
  • J. Brodzki, V. Mathai, J. Rosenberg and R. Szabo, D-Branes, RR-Fields and Duality on Noncommutative Manifolds, Communications in Mathematical Physics, 277, no.3 (2008) 643-706. [hep-th/0607020]
  • All Recent Publications

    • FAA Fellow, Australian Academy of Science 
    • FAustMS Fellow, Australian Mathematical Society
    • FRSSA Fellow, Royal Society of South Australia

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    Entry last updated: Wednesday, 26 Jul 2017

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