Mathai Varghese

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

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.

 

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.

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 - 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 Analytic Pontryagin Duality Doctor of Philosophy Doctorate Full Time Mr Johnny Khai Yang Lim
    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
  • 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

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