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Mathai Varghese is a mathematician at the University of Adelaide . His first most influential contribution is the Mathai–Quillen formalism ,[6] Daniel Quillen , and which has since found applications in 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 .[7] 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 ARC Australian Laureate Fellowship .[8] Hannan Medal [9] George Szekeres Medal [10]
Biography [ edit ]
Mathai studied at Bishop Cotton Boys' School, Bangalore . Mathai received a BA 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 Medallist .
Mathai's work is in the area of geometric analysis . His research interests are in
L
2
{\displaystyle L^{2}}
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.[11] Jonathan Rosenberg , on T-duality in the presence of background flux.[12]
The Mathai–Quillen formalism appeared in Topology superconnection formalism of Quillen, they obtained a refinement of the 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 functions for the fermionic analogue of a harmonic oscillator with source term. In particular, they obtained a nice 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 .[citation needed
Mathai was awarded the Australian Mathematical Society Medal in 2000.[13] 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 [ edit ]
Mathai, Varghese; Quillen, Daniel (1986). "Superconnections, Thom classes and equivariant differential forms". Topology 25 1 ): 85–110. doi :10.1016/0040-9383(86 )90007-8 .
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. ; Singer, Isadore M. (2006). "Fractional Analytic Index" . Journal of Differential Geometry 74 2 ): 265–292. arXiv :math/0402329 doi :10.4310/jdg/1175266205
^ "2017 Laureate Profile: Professor Mathai Varghese" .
^ "2021 Hannan medal and Lecture: Professor Mathai Varghese" .
^ "2021 George Szekeres medal: Professor Mathai Varghese" .
^ Mathai, Varghese and Quillen, Daniel. (1986) "Superconnections, Thom classes and equivariant differential forms". Topology 25 1 ), 85–110.
^ "Fellows elected in 2011" . Australian Academy of Science. Archived from the original on 27 May 2012. Retrieved 15 March 2012 .
^ "2017 Laureate Profile: Professor Mathai Varghese" .
^ "2021 Hannan medal and Lecture: Professor Mathai Varghese" .
^ "2021 George Szekeres medal: Professor Mathai Varghese" .
^ Mathai, Varghese; Melrose, Richard B.; Singer, Isadore M. (2006). "Fractional Analytic Index" . Journal of Differential Geometry . 74 2 ): 265–292. arXiv :math/0402329 doi :10.4310/jdg/1175266205
^ Bouwknegt, Peter, Evslin, Jarah and Mathai, Varghese. (2004) "T-duality: Topology Change from H-flux". Communications in Mathematical Physics 249 (2 ), 383–415.
^ "Christine O'Keefe and Mathai Varghese share the Australian Mathematical Society 2000 Medal" . Australian Mathematical Society.
References [ edit ]
External links [ edit ]
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R e t r i e v e d f r o m " https://en.wikipedia.org/w/index.php?title=Varghese_Mathai&oldid=1193767539 " C a t e g o r i e s : ● 2 0 t h - c e n t u r y I n d i a n m a t h e m a t i c i a n s ● 2 1 s t - c e n t u r y I n d i a n m a t h e m a t i c i a n s ● A u s t r a l i a n m a t h e m a t i c i a n s ● A u s t r a l i a n p e o p l e o f M a l a y a l i d e s c e n t ● M a s s a c h u s e t t s I n s t i t u t e o f T e c h n o l o g y a l u m n i ● I l l i n o i s I n s t i t u t e o f T e c h n o l o g y a l u m n i ● S c i e n t i s t s f r o m K e r a l a ● A c a d e m i c s t a f f o f t h e U n i v e r s i t y o f A d e l a i d e ● L i v i n g p e o p l e ● F e l l o w s o f t h e A u s t r a l i a n A c a d e m y o f S c i e n c e H i d d e n c a t e g o r i e s : ● U s e d m y d a t e s f r o m A u g u s t 2 0 1 5 ● U s e A u s t r a l i a n E n g l i s h f r o m A u g u s t 2 0 1 5 ● A l l W i k i p e d i a a r t i c l e s w r i t t e n i n A u s t r a l i a n E n g l i s h ● A r t i c l e s w i t h h C a r d s ● A l l a r t i c l e s w i t h u n s o u r c e d s t a t e m e n t s ● A r t i c l e s w i t h u n s o u r c e d s t a t e m e n t s f r o m A p r i l 2 0 1 8 ● A r t i c l e s w i t h M A T H S N i d e n t i f i e r s ● A r t i c l e s w i t h M G P i d e n t i f i e r s ● A r t i c l e s w i t h O R C I D i d e n t i f i e r s ● A r t i c l e s w i t h Z B M A T H i d e n t i f i e r s ● Y e a r o f b i r t h m i s s i n g ( l i v i n g p e o p l e )
● T h i s p a g e w a s l a s t e d i t e d o n 5 J a n u a r y 2 0 2 4 , a t 1 4 : 5 0 ( U T C ) . ● T e x t i s a v a i l a b l e u n d e r t h e C r e a t i v e C o m m o n s A t t r i b u t i o n - S h a r e A l i k e L i c e n s e 4 . 0 ;
a d d i t i o n a l t e r m s m a y a p p l y . B y u s i n g t h i s s i t e , y o u a g r e e t o t h e T e r m s o f U s e a n d P r i v a c y P o l i c y . W i k i p e d i a ® i s a r e g i s t e r e d t r a d e m a r k o f t h e W i k i m e d i a F o u n d a t i o n , I n c . , a n o n - p r o f i t o r g a n i z a t i o n . ● P r i v a c y p o l i c y ● A b o u t W i k i p e d i a ● D i s c l a i m e r s ● C o n t a c t W i k i p e d i a ● C o d e o f C o n d u c t ● D e v e l o p e r s ● S t a t i s t i c s ● C o o k i e s t a t e m e n t ● M o b i l e v i e w
