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,
2) election as Fellow of the Australian Academy of Science in 2011,
3) the award of the prestigious Australian Laureate Fellowship (2018-2022),
4) award of the 2021 Hannan medal and Lecture from the Australian Academy of Science,
5) award of the 2021 George Szekeres medal from the Australian Mathematical Society.
6) presented the 2022 Professional Achievement Award, Illinois Institute of Technology (Chicago).
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.
- My Research
- Grants and Funding
- Professional Activities
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.
Date Position Institution name 2018 - 2022 Australian Laureate Fellow University of Adelaide 2013 - ongoing Sir Thomas Elder Professor of Mathematics University of Adelaide 2009 - ongoing Director of the Institute for Geometry and its Applications (IGA) University of Adelaide 2007 - ongoing Adjunct Professor of Mathematics Australian National University
Awards and Achievements
Date Type Title Institution Name Country Amount 2022 Award Professional Achievement Award Illinois Institute of Technology United States - 2021 Award George Szekeres medal Australian Mathematical Society Australia - 2021 Research Award Hannan medal and Lecture Australian Academy of Science Australia - 2018 Fellowship Australian Laureate Fellowship University of Adelaide Australia $1.64 million 2013 Award Discovery Outstanding Researcher Award University of Adelaide Australia $630,000 2013 Fellowship Fellow of the Royal Society of South Australia Royal Society of South Australia Australia - 2011 Fellowship Fellow of the Australian Academy of Science, FAA Australian Academy of Science Australia - 2007 Fellowship Australian Professorial Fellowship University of Adelaide Australia $500,000 2006 Fellowship Senior Research Fellowship Erwin Schrodinger Institute for Mathematical Physics Austria - 2001 Fellowship ARC Senior Research Fellowship University of Adelaide Australia - 2000 Award Medal, Australian Mathematical Society Australian Mathematical Society Australia - 2000 Fellowship Fellow, Australian MathematicalSociety, FAustMS AustralianMathematicalSociety Australia - 2000 Fellowship Clay Mathematics Institute Research Fellowship Massachusetts Institute of Technology United States - 1994 Fellowship Australian Research Fellowship University of Adelaide Australia -
Date Institution name Country Title 1986 Massachusetts Institute of Technology United States PhD (Pure Mathematics) 1981 Illinois Institute of Technology United States BA (Mathematics)
Date Title Institution Country 1981 - 1986 PhD in Mathematics Massachusetts Institute of Technology United States
Research InterestsAlgebraic and Differential Geometry Conformal Field Theory Field Theory and String Theory K Theory Mathematical Aspects of Condensed Matter Mathematical Aspects of Quantum Mathematical Physics Operator Algebras and Functional Analysis Partial Differential Equations Pure Mathematics Quantum Gravity and String Theory Quantum Physics Topology
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)
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
Date Role Committee Institution Country 2015 - 2018 Member Sectional Committee 1: Mathematical Sciences Australian Academy of Science Australia 2015 - 2017 Member Elizabeth And Frederick White Research Conferences Awards Committee Australian Academy of Science Australia 2011 - 2012 Chair Gavin Brown Prize committee Australian Mathematical Society Australia 2007 - 2009 Chair Mahler Lecturer committee Australian Mathematical Society Australia 2006 - 2009 Vice-President Steering committee Australian Mathematical Society Australia 2006 - 2009 Vice-President AustMS conferences program committee Australian Mathematical Society Australia
Date Role Editorial Board Name Institution Country 2018 - 2019 Editor-In-chief Journal of Geometry and Physics Elsevier Netherlands 2017 - 2018 Editor-In-chief Journal of Geometry and Physics Elsevier Netherlands 2016 - ongoing Editor Letters in Journal of Geometry and Physics Elsevier Netherlands 2014 - ongoing Editor Journal of Geometry and Physics Elsevier Netherlands 2010 - 2011 Editor Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics Cambridge University Press, Cambridge, UK. Australia 2010 - 2014 Board Member Advisory Board Australian Mathematical Society Australia 2008 - 2016 Editor Proceedings of the American Mathematical Society American Mathematical Society, Providence, Rhode Island United States
Date Office Name Institution Country 2006 - 2009 Vice President in charge of annual conferences Australian Mathematical Society Australia
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