Professor Mathai Varghese
Position  Elder Professor of Mathematics 

Org Unit  Mathematical Sciences 
mathai.varghese@adelaide.edu.au  
Telephone  +61 8 8313 4173 
Location 
Floor/Room
7 31
,
Ingkarni Wardli
,
North Terrace


Biography/ Background
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.
3year 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)
201718, Managing Guest Editor, JGP special issue on Noncommutative Geometry 2017: a celebration of Alain Connes 70th birthday
201617, 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)

Qualifications
 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)

Awards & Achievements
2017, Australian Laureate Fellowship
2016, Herbert Howe Lecture series, Department of Mathematics, University of Denver, Denver, Colorado (May 1720).
See this link for a report on the public lecture , or the AAS newsletter item.20162018, 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. 20152017, Member, Elizabeth and Frederick White Research Awards Committee,
Australian Academy of Science. Further information on the award can be found here. 2013current, Sir Thomas Elder Chair, full Professor (level E), University of Adelaide, Adelaide.20132015, awarded ARC Discovery Outstanding Researcher Award. ,
2011, elected Fellow, Australian Academy of Science;
2009  current, Director, Institute for Geometry and its Applications, University of Adelaide, Adelaide;
2009, Chair, selection committee for the Mahler Lecturer.
20072011, awarded ARC Professorial Fellowship. ,
20062009, 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. 
Research Interests
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

Research Funding
ARC Discovery Project grants (current) :
Parametrised gauge theory and positive scalar curvature,
(jointly with D. Baraglia, Jan. 2017 Dec. 2019, $335K awarded)Ubiquity of Ktheory and Tduality
(jointly with P. Bouwknegt, Jan. 2015 Dec. 2017, $370K awarded).All recent ARC Discovery Project grants and Postdoc supervision

Publications
Mathai has coauthored 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) 18591922, [1210.0990]
V. Mathai and J. Rosenberg, Group dualities, Tdualities, and twisted Ktheory, Journal of the London Mathematical Society, (to appear) 29 pages, [1603.00969]
V. Mathai and G. C. Thiang, Differential topology of semimetals, Communications in Mathematical Physics, 355 , no. 2,(2017) 561602. [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 Spin^{c}manifolds, Asian Journal of Mathematics, 21 no. 4 (2017) 631686. [1408.0085]
K. Hannabuss, V. Mathai, G. C. Thiang, Tduality simplifies bulkboundary correspondence: the parametrised case, Advances in Theoretical and Mathematical Physics, 20 no. 5 (2016) 11931226, [1510.04785]
P. Hochs, V. Mathai, Formal geometric quantisation for proper actions, Journal of Homotopy and Related Structures, 11 , no.3, (2016) 409424, [1403.6542]
V. Mathai, G.C. Thiang, Tduality simplifies bulkboundary correspondence: some higher dimensional cases, Annales Henri Poincare, 17 no. 12 (2016) 3399–3424, [1506.04492]
V. Mathai and G. C. Thiang, Tduality simplifies bulkboundary correspondence, Communications in Mathematical Physics, 345 no. 2, (2016) 675701 [1505.05250]
P. Hochs and V. Mathai, Spin manifolds and proper group actions, Advances in Mathematics, 292 (2016) 110, [1411.0781]
MT. Benameur and V. Mathai, Spectral sections, twisted rho invariants and positive scalar curvature, Journal of Noncommutative Geometry, 9 , no. 3, (2015) 821850, [1309.5746]
V. Mathai and G.C. Thiang, Tduality 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) 362426, [1309.6760]
A. Linshaw and V. Mathai, Twisted Chiral De Rham Complex, Generalized Geometry, and Tduality, Communications in Mathematical Physics, 339, No. 2, (2015) 663697, [1412.0166]
P.Bouwknegt, J.Evslin and V.Mathai, Spherical Tduality, Communications in Mathematical Physics, 337, No. 2, (2015) 909954. [1405.5844]
V.Mathai and H.Sati, Higher abelian gauge theory associated to gerbes on noncommutative deformed M5branes and Sduality, Journal of Geometry and Physics, 92 (2015) 240251, [1404.2257]
P.Bouwknegt, J.Evslin and V.Mathai, Spherical Tduality II: An infinity of spherical Tduals for nonprincipal SU(2)bundles, J. Geometry and Physics, 92 (2015) 4654, [1409.1296]
F. Han, V. Mathai, Exotic twisted equivariant cohomology of loop spaces, twisted BismutChern character and Tduality, Communications in Mathematical Physics, 337 , No. 1, (2015) 127150. [1405.1320]
V. Mathai, J. Rosenberg, Tduality for circle bundles via noncommutative geometry, Advances in Theoretical and Mathematical Physics, 18 , no. 6 (2014) 14371462, [1306.4198]
MT. Benameur, V. Mathai, Index type invariants for twisted signature complexes and homotopy invariance, Mathematical Proceedings of the Cambridge Philosophical Society, 156 no.3 (2014) 473503, [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), 785794, [1202.5213]
MT. Benameur, V. Mathai, Conformal invariants of twisted Dirac operators and positive scalar curvature J. Geometry and Physics, 70 (2013) 3947, [1210.0301] Erratum , J. Geometry and Physics, 76 (2014) 263264.
V. Mathai and S. Wu, Topology and Flux of TDual Manifolds with Circle Actions, Communications in Mathematical Physics, 316 (2012) 279286. [1108.5045]
P. Bouwknegt, V. Mathai and S. Wu, Bundle gerbes and moduli spaces, J. Geometry and Physics,, 62 no.1, (2012) 110, [1107.3687]
V. Mathai and S.Wu, Analytic torsion for twisted de Rham complexes, J. Differential Geometry, 88 (2011) 297332, [0810.4204]
V. Mathai and J. Rosenberg, A noncommutative sigmamodel, J. Noncommutative Geometry, 5 no 2 (2011) 265294, [0903.4241]
V. Mathai, W. Zhang, Geometric quantization for proper actions, Advances in Mathematics, 225 no.3 (2010) 12241247 [0806.3138v2]
P. Bouwknegt, K. Hannabuss, V. Mathai, C*algebras in tensor categories, Clay Mathematics Proceedings, 12 (2010) 127165. [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) 255296, [0809.0028]
P. Chakraborty, V. Mathai, The geometry of determinant line bundles in noncommutative geometry, J. Noncommutative Geometry, 3 no.4 (2009) 559578. [0804.3232v2]
J. Brodzki, V. Mathai, J. Rosenberg, R. Szabo, Noncommutative correspondences, duality and Dbranes in bivariant Ktheory, Advances in Theoretical and Mathematical Physics, 13 no. 2 (2009) 497552. [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) 465473. [math.DG/0611819]
J. Brodzki, V. Mathai, J. Rosenberg and R. Szabo, DBranes, RRFields and Duality on Noncommutative Manifolds, Communications in Mathematical Physics, 277 , no.3 (2008) 643706. [hepth/0607020]

Professional Associations
 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: Thursday, 9 Aug 2018
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