Varghese Mathai: Difference between revisions

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'''Mathai Varghese''' is a mathematician at the [[University of Adelaide]]. His first most influential contribution is the [[Mathai–Quillen formalism]],<ref> Mathai, Varghese and Quillen, Daniel. (1986) "Superconnections, Thom classes and equivariant differential forms". ''Topology'' '''25''' (1), 85–110.</ref> which he formulated together with [[Daniel Quillen]], and which has since found applications in [[Atiyah-Singer index theorem|index theory]] and [[topological quantum field theory]]. He was appointed a full professor in 2006. He was appointed Director of the [[Institute for Geometry and its Applications]] in 2009. In 2011, he was elected a [[Fellow of the Australian Academy of Science]].<ref>{{cite web|url=http://www.science.org.au/fellows/elected/2011.html|title=Fellows elected in 2011|publisher=Australian Academy of Science|access-date=15 March 2012|archive-url=https://web.archive.org/web/20120527151019/http://science.org.au/fellows/elected/2011.html|archive-date=27 May 2012|url-status=dead|df=dmy-all}}</ref> In 2013, he was appointed the (Sir Thomas) [[Elder Professor of Mathematics]] at the University of Adelaide, and was elected a Fellow of the Royal Society of South Australia. In 2017, he was awarded an [[Australian Research Council|ARC]] [[Australian Laureate Fellowship]].<ref>{{cite web|url=http://www.arc.gov.au/2017-laureate-profile-professor-mathai-varghese|title=2017 Laureate Profile: Professor Mathai Varghese}}</ref>

In 2021, he was awarded the prestigious [[Hannan Medal]]<ref>{{cite web|url=https://www.science.org.au/supporting-science/awards-and-opportunities/hannan-medal|title=2021 Hannan medal and Lecture: Professor Mathai Varghese}}}</ref> and Lecture from the Australian Academy of Science, recognizing an outstanding career in Mathematics. In 2021, he was also awarded the prestigious [[George Szekeres Medal]]<ref>{{cite web|url=https://austms.org.au/awards-grants/awards/the-george-szekeres-medal/|title=2021 George Szekeres medal: Professor Mathai Varghese}}}</ref>

which is the Australian Mathematical Society’s most prestigious medal, recognising research achievement and an outstanding record of promoting and supporting the discipline.

Mr Mathai studied at Bishop Cotton Boy's School, Bangalore. Mathai received a [[Bachelor of Arts|BA]] at the [[Illinois Institute of Technology]]. He then proceeded to the [[Massachusetts Institute of Technology]], where he was awarded a [[doctorate]] under the supervision of [[Daniel Quillen]], a [[Fields Medal]]list.

Mathai's work is in the area of [[geometric analysis]]. His research interests are in <math>L^2</math> analysis, index theory, and [[noncommutative geometry]]. He currently works on mathematical problems that have their roots in physics, for example, topological field theories, [[fractional quantum Hall effect]], and [[D-branes]] in the presence of [[B-fields]]. The main focus of his research is on the application of noncommutative geometry and index theory to mathematical physics, with particular emphasis on [[string theory]]. His current work on index theory is ongoing joint work with [[Richard Burt Melrose|Richard Melrose]] and [[Isadore Singer]], on the fractional analytic index and on the index theorem for projective families of elliptic operators.<ref>{{cite journal |author1= Mathai, Varghese |author2= Melrose, Richard B. |author3= Singer, Isadore M. |year=2006 |title= Fractional Analytic Index |journal= Journal of Differential Geometry |volume=74 |number=2 |pages= 265–292 | arxiv=math/0402329| doi=10.4310/jdg/1175266205|doi-access= free }}</ref>  His current work on string theory is ongoing joint work with Peter Bouwknegt, Jarah Evslin, Keith Hannabuss and [[Jonathan Rosenberg (mathematician)|Jonathan Rosenberg]], on T-duality in the presence of background flux.<ref>Bouwknegt, Peter, Evslin, Jarah and Mathai, Varghese. (2004) "T-duality: Topology Change from H-flux". ''Communications in Mathematical Physics'' '''249''' (2), 383–415.</ref>

The Mathai–Quillen formalism appeared in ''[[Topology (journal)|Topology]]'', shortly after Mathai completed his Ph.D. Using the [[superconnection]] formalism of Quillen, they obtained a refinement of the [[Riemann–Roch theorem|Riemann–Roch formula]], which links together the [[Thom space|Thom classes]] in [[K-theory]] and [[cohomology]], as an equality on the level of differential forms. This has an interpretation in physics as the computation of the classical and quantum (super) [[partition function (statistical mechanics)|partition functions]] for the fermionic analogue of a [[harmonic oscillator]] with source term. In particular, they obtained a nice [[Gaussian function|Gaussian shape]] representative of the [[Thom class]] in cohomology, which has a peak along the zero section. Its universal representative is obtained using the machinery of [[equivariant differential forms]].{{cn|date=April 2018}}