Mudumbai Narasimhan has made outstanding contributions to an area of mathematics including algebraic and differential geometry, the representation theory of Lie groups, and the theory of partial differential equations. He is best known for his theorem of 1965 (with C. S. Seshadri) proving that holomorphic bundles on an algebraic curve come from unitary representations of its fundamental group. This opened up a whole avenue of progress which is still proving remarkably fruitful. Mudumbai has continued to be a leader in the study of moduli spaces of holomorphic bundles, but apart from that his work with Sundararaman Ramanan on universal connections has proved influential, and he also (with Kiyosato Okamoto) proved the first case of Langland’s conjecture about the realisation of the discrete series of representations of a Lie group.

Professor Mudumbai Narasimhan FRS died on 15 May 2021.