Mathai Varghese

Professor Mathai Varghese

Elder Prof. Maths & Aust Laureate Fellow

School of Mathematical Sciences

Faculty of Engineering, Computer and Mathematical Sciences

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 election to the Australian Academy of Science in 2011 and award of the prestigious Australian Laureate Fellowship (2018-2022). Professor Varghese has published over 100 scientific articles 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.

 

My recent research interests include: index theory of elliptic operators; secondary invariants of elliptic operators; geometric quantization: noncompact context; and noncommutative geometry. Recently my interests include gauge theory as well as topological obstructions to the existence of positive scalar curvature metrics on compact spin manifolds.

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 http://iopscience.iop.org/journal/1751-8121/labtalk/article/63194 ; 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)

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). 

Differential Topology
Honours and MPhil level course, 
University of Adelaide, 
Taught in 2016, 2017.

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  • Current Higher Degree by Research Supervision (University of Adelaide)

    Date Role Research Topic Program Degree Type Student Load Student Name
    2018 Principal Supervisor Computations in Higher Twisted K-theory Master of Philosophy Master Full Time Mr David Leonard Brook
    2018 Principal Supervisor Seibert-Witten Equations and Pseudo-holomorphic Curves Applied to Superconductors and Particle Physics Master of Philosophy Master Full Time Mr Ahnaf Tajwar Tahabub
    2017 Principal Supervisor Pontryagin Duality in Higher Aharonov-Bohm Effect Doctor of Philosophy Doctorate Full Time Mr Johnny Khai Yang Lim
    2017 Principal Supervisor Non-Commutative Index Theory on Singular Spaces Master of Philosophy Master Full Time Mr Samuel Mills
  • Past Higher Degree by Research Supervision (University of Adelaide)

    Date Role Research Topic Program Degree Type Student Load Student Name
    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
    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
    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: Elder Prof. Maths & Aust Laureate Fellow
  • Phone: 83134173
  • Email: mathai.varghese@adelaide.edu.au
  • Fax: 8313 3696
  • Campus: North Terrace
  • Building: Ingkarni Wardli, floor 7
  • Room: 7 31
  • Org Unit: Mathematical Sciences

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