S. Ramanan

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Sundararaman Ramanan (* 1936 in Thiruvannamalai in Tamil Nadu ) is an Indian mathematician who specializes in algebraic geometry , differential geometry and Lie groups .

life and work

Ramanan attended school in Chennai (Vivekananda College), received a bachelor's degree in mathematics from the University of Madras, and received his PhD from the University of Mumbai and the Tata Institute of Fundamental Research (where he was since 1957) with MS Narasimhan in 1966 ( Geometry of Fiber Bundles- Homogeneous Vector Bundles ). He was then professor at the Tata Institute until 2002, where he worked with MS Narasimhan for many years. After his retirement at the Tata Institute, he was adjunct professor at the Chennai Mathematical Institute and visiting professor at the Institute of Mathematical Sciences in Chennai.

He dealt with vector space bundles on algebraic curves (Riemann surfaces) and their module spaces (often in collaboration with Narasimhan), geometric invariant theory, Abelian varieties, Flaggen and Schubert varieties (with vector space bundles on them) and Higgs bundles. In differential geometry, his existence theorem of universal connections with Narasimhan was influential, for example in the work of SS Chern and James Simons . In differential geometry he was influenced by Jean-Louis Koszul , whose lectures at the Tata Institute he heard and edited in 1965.

Vijay Kumar Patodi is one of his students (whose dissertation he was supervising with Narasimhan). He also worked with the a few years younger A. Ramanathan at the Tata Institute, for example on flag varieties.

He received the Shanti Swarup Bhatnagar Prize (1979), the Third World Academy of Sciences Prize in Mathematics (2001), and the Indian National Science Academy's Srinivasa Ramanujan Medal (2008). In 1978 he was invited speaker at the International Congress of Mathematicians in Helsinki ( Vector Bundles over Algebraic Curves ). In 1977/78 he was at the Institute for Advanced Study . He is a Fellow of the Indian Academy Sciences, the Indian National Science Academy, and the National Academy of Sciences, India.

He is married and has two daughters, one is a journalist for the Hindustan Times in Mumbai and one daughter (Kavita) is a math professor at Brown University .

Fonts

  • with MS Narasimhan: Existence of universal connections. American Journal of Mathematics, Volume 83, 1961, pp. 563-572
  • with MS Narasimhan Moduli of vector bundles over a compact Riemann surface , Annals of Mathematics, Volume 89, 1969, pp. 14-51
  • with MS Narasimhan Vector bundles on curves , in Algebraic Geometry , International Colloquium, Tata Institute, Bombay, Oxford University Press 1968, pp. 335-346
  • with MS Narasimhan Deformations of the moduli space of vector bundles over an algebraic curve , Annals of Mathematics, Volume 101, 1975, pp. 391-417
  • The moduli space of vector bundles over an algebraic curve , Mathematische Annalen, Volume 200, 1973, pp. 69-84
  • with Usha V. Desale Poincaré polynomials of the variety of stable bundles , Mathematische Annalen, Volume 216, 1975, pp. 233–244
  • with Desale Classification of vector bundles of rank 2 on hyperelliptic curves , Inventiones Mathematicae, Volume 38, 1976/77, pp. 161-185
  • with A. Ramanathan Some remarks on the instability flag , Tohoku Math. J., Volume 36, 1984, pp. 269-291
  • Ample divisors on abelian surfaces , Proc. London Math. Society, Vol. 51, 1985, pp. 231-245
  • with A. Ramanathan Projective normality of flag varieties and Schubert varieties , Inventiones Mathematicae, Volume 79, 1985, pp. 217-224
  • with Arnaud Beauville , MS Narasimhan Spectral curves and the generalized theta divisor , J. Reine Angew. Math., Vol. 398, 1989, pp. 169-179
  • Global Calculus , American Mathematical Society 2005
  • with Allan Adler Moduli of Abelian Varieties , Lecture Notes in Mathematics 1644, Springer-Verlag, 2009

literature

  • MS Narasimhan The work of S. Ramanan , Contemporary Mathematics, Online, pdf

Web links

Individual evidence

  1. ^ Mathematics Genealogy Project
  2. ↑ Narasimhan, Ramanan Existence of universal connections , 1,2, American J. Math., Vol. 83, 1961, pp. 563-572, Vol. 85, 1963, pp. 223-231
personal data
SURNAME Ramanan, S.
ALTERNATIVE NAMES Ramanan, Sundararaman (full name)
BRIEF DESCRIPTION Indian mathematician
DATE OF BIRTH 1936
PLACE OF BIRTH Thiruvannamalai , Tamil Nadu