Narasimhan started his career in 1960 when he joined the faculty of the
Tata Institute of Fundamental Research (TIFR); he later went on to become an honorary fellow. His areas of focus while at TIFR included studying
partial differential operators and
elliptic operators. He collaborated with Indian mathematician
C. S. Seshadri for the ground-breaking
Narasimhan–Seshadri theorem which has been at the core of algebraic geometry and number theory for over half a century. The theorem derived the relation between the purely algebraic notion of
stable vector bundles on
Riemann surfaces. For his work, Narasimhan was considered a pioneer in the study of
moduli spaces of
holomorphic vector bundles on
projective varieties. After retiring from ICTP, he settled in
Bangalore. He was awarded the
Padma Bhushan, India's third highest civilian honor, in 1990. He was also the recipient of the
Shanti Swarup Bhatnagar Prize in 1975,
Third World Academy of Sciences Prize for Mathematics in 1987, and the
Srinivasa Ramanujan Medal in 1988. He was also the recipient of the
King Faisal International Prize for Science in 2006, an award that he won jointly with mathematician
Simon Donaldson, Imperial College. As of 2021, he was the only Indian to have won the King Faisal International Prize for Science. Also in 2021, he became a laureate of the
Asian Scientist 100 by the
Asian Scientist. == Personal life ==