en>Vinícius Machado Vogt at 21:09, 30 December 2014

2014-12-30T21:09:48Z

en>David Eppstein: Pretty sure this is notable, and I don't see the point of the undue tag. But tag for lack of references.

2013-10-03T03:08:49Z

Pretty sure this is notable, and I don't see the point of the undue tag. But tag for lack of references.

New page

{{Western name order|Mathai Varghese}}
'''Mathai Varghese''' is a mathematician and an [[Australian Research Council]] (ARC) Discovery Outstanding Research Fellow at the [[University of Adelaide]]. His most influential contribution to date 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 became a full professor in 2006. He became Director of the [[Institute for Geometry and its Applications]] in 2009. In 2011, he was elected 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 Sciences}}</ref> In 2013, he was appointed the (Sir Thomas) Elder Chair in Mathematics <ref>{{cite web|url=http://en.wikipedia.org/wiki/Thomas_Elder#Elder_Professor_of_Mathematics|title=Elder Chairs in Mathematics}}</ref> and was elected Fellow of the Royal Society of South Australia.

Mathai received his [[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|Fields medallist]].

Mathai's work may be considered to fall under the ambit 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 Melrose and [[Isadore Singer]], on the fractional analytic index and on the index theorem for projective families of elliptic operators. <ref>Mathai, Varghese, Melrose, Richard B. and Singer, Isadore M.. (2006) "Fractional Analytic Index". ''Journal of Differential Geometry'' '''74''' (2), 265–292.</ref>
His current work on string theory is ongoing joint work with Peter Bouwknegt, Jarah Evslin, Keith Hannabuss and 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]] shortly after Mathai completed his PhD. Using the [[superconnection]] formalism of Quillen, they obtained a refinement of the [[Riemann-Roch theorem|Riemann–Roch formula]], which links together the 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 shaped]] 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]].

Mathai was awarded the [[Australian Mathematical Society]] Medal in 2000.<ref>{{cite web|url=http://oldsite.austms.org.au/AMSInfo/Medal/2000winners.html|title=Christine O'Keefe and Mathai Varghese share the Australian Mathematical Society 2000 Medal|publisher=Australian Mathematical Society}}</ref> From August 2000 to August 2001, he was also a [[Clay Mathematics Institute]] Research Fellow and Visiting Scientist at the [[Massachusetts Institute of Technology]]. From March to June 2006, he was a Senior Research Fellow at the [[Erwin Schrödinger Institute]] in Vienna.

==Selected publications==
* Mathai, Varghese and Quillen, Daniel. (1986) "Superconnections, Thom classes and equivariant differential forms". ''Topology'' '''25''' (1), 85–110.
* Bouwknegt, Peter, Evslin, Jarah and Mathai, Varghese. (2004) "T-duality: Topology Change from H-flux". ''Communications in Mathematical Physics'' '''249''' (2), 383–415.
* Mathai, Varghese, Melrose, Richard B. and Singer, Isadore M.. (2006) "Fractional Analytic Index". ''Journal of Differential Geometry'' '''74''' (2), 265–292.

==Notes==

{{Reflist}}

==References==

* Blau, Matthias [http://arxiv.org/abs/hep-th/9203026 "The Mathai-Quillen Formalism and Topological Field Theory"], Infinite-dimensional geometry in physics (Karpacz, 1992). J. Geom. Phys. 11 (1993), no. 1-4, 95–127
* Wu, Siye [http://arxiv.org/abs/hep-th/0505003 "Mathai-Quillen Formalism"], J. Geom. Phys. 17 (1995), no. 4, 299–309

==External links==
* [http://www.maths.adelaide.edu.au/mathai.varghese/ Mathai Varghese's homepage] at the University of Adelaide.
* {{MathGenealogy|id=62771}}

{{Persondata 
| NAME = Mathai, Varghese
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = Australian mathematician
| DATE OF BIRTH =
| PLACE OF BIRTH =
| DATE OF DEATH =
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Mathai, Varghese}}
[[Category:20th-century mathematicians]]
[[Category:21st-century mathematicians]]
[[Category:Australian mathematicians]]
[[Category:Australian people of Indian descent]]
[[Category:Illinois Institute of Technology alumni]]
[[Category:Kerala scientists]]
[[Category:University of Adelaide faculty]]
[[Category:Year of birth missing (living people)]]
[[Category:Living people]]

Three-torus - Revision history

en>Vinícius Machado Vogt at 21:09, 30 December 2014

en>David Eppstein: Pretty sure this is notable, and I don't see the point of the undue tag. But tag for lack of references.