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Name: Vishwambhar Pati


Date of Birth: 27 September, 1957


Designation: Professor


Doctorate: Princeton University, NJ, USA, 1985.


PUBLICATIONS:

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(with W.-C. Hsiang), $ L^{2}$-cohomology of Normal Algebraic Surfaces I, Inventiones Mathematicae, 81, 395-412 (1985), MR 0807064 (87f:32024).


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$ L^{2}$-cohomology of Algebraic Varieties in the Fubini Metric, Proceedings of the Conference on Hodge Theory, Sant Cugat, Spain, Springer Lecture Notes in Mathematics No. 1246, 154-164, (1986), MR 0894050 (88i:32020).


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Some Basic Facts on Algebraic Curves, (expository article), Current Science (Indian Academy of Sciences) Vol. 61, No. 2, 82-88, (1991).


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The Heat Trace on Singular Algebraic Threefolds, Journal of Differential Geometry, Vol. 37, No. 1, 245-261 (1993), MR 1198608 (94c:58201).


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(with Gadadhar Misra), Contractive and Completely Contractive Modules, Matricial Tangent Vectors and Distance-decreasing Metrics, Journal of Operator Theory, Vol. 31, 1-28, (1993), MR 1305512 (95j:46092).


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(with R. Bhat and V.S. Sunder),On the Extreme Points of Some Convex Sets, Mathematische Annalen 296, 637-648 (1993), MR 1233488 (94f:46076).


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The Laplacian on Algebraic Threefolds with Isolated Singularities, Proc. Indian Acad. Sci. (Math. Sci.), Vol. 104, No 3, 435-481, (1994), MR 1314391 (96a:32064).


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(with M. Shahshahani and A. Sitaram), The Spherical Mean Value Operator on Compact Symmetric Spaces, Pacific Jour. Math., Vol 168, No. 2, 335-344, (1995), MR 1339956 (96f:58163).


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The Punctured Plane (expository article) in Resonance, Journal of Science Education published by the Indian Academy of Sciences, Vol. 1, No. 4, 37-49, (1996).


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(with A. Sitaram, M. Sundari, S. Thangavelu), Eigenfunction expansions and the Uncertainty Principle, Journal of Fourier Analysis and Applications, Vol. 2, No. 5, 427-433, (1996), MR 1412061 (98g:42046).


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(with Kapil Paranjape), Seiberg-Witten Invariants-an Expository Account, Proc. Indian Acad. Sci. (Math. Sci.), Vol. 109, No. 3, 257-270, (1999), (electronic version: xxx.lanl. gov/ pdf /math.DG 9809044, 1998), MR 1709333 (2000h:57060).


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The Theorem of Kronheimer-Mrowka (expository), Proc. Indian Acad. Sci. (Math. Sci.), Vol. 109, No. 3, 271-298, (1999), (electronic version: xxx.lanl.gov/ pdf/ math.DG 9809045, 1998), MR 1709334 (2000h:57061).


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Hilbert's Nullstellensatz (expository article) in Resonance, Journal of Science Education, Vol. 4, No. 8, 36-57, (1999).


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(with A. Sitaram) Some Questions on Integral Geometry on Riemannian Manifolds, Sankhya, Series A, Vol. 62, Part 3, 419-424, (2000) (Volume in honour of M.G. Nadkarni), MR 1803467 (2002d:53102).


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Unitary Tridiagonalisation in $ M(4, {\bf C})$, Proc. Indian Acad. Sci. (Math. Sci.), Vol 111. No. 4, 381-397, (2001), electronic version: xxx.lanl.gov/ pdf / math.RA0109051, 2001), MR 1923981 (2003k:15011).


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The Uncertainty Principle on Riemannian Manifolds, in Analysis and its Applications, Proceedings of a Conference in honor of Prof. T. Pati, held in Feb. 2000, edited by H.P.Dikshit and P.K.Jain, Narosa Publishing House 251-266, (2002), MR 1970598 (2004f:58041).


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Subanalytic Bundles and Tubular Neighbourhoods of Zero-loci, Proc. Indian Acad. Sci. (Math. Sci.), Vol 113, No. 3, (2003), 381-397 (electronic version: xxx.lanl.gov/pdf/math.AG 0307021), MR 1999256 (2004g:32009).


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(with V. Kodiyalam and V.S. Sunder)Subfactors and 1+1-Dimensional TQFTS, The International Journal of Mathematics, Vol 18, No. 1, (2007), 69-112, MR 2294417 (2008a:46063).


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(with P. Pragacz and V. Srinivas) Diagonal Subschemes and Vector Bundles,Pure and Applied Mathematics Quarterly, (Special Issue in honour of J-P Serre, Vol 4, No. 4, (2008), 1233-1278, MR 2441700 (2009f:14084).


BOOKS:

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Book edited jointly with A. Sitaram, Mathematical Analysis, in the series "Echoes from Resonance, Universities Press, Hyderabad (2001).