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Name Professor SG Dani
(Professor Shrikrishna Gopalrao Dani)
FNA ID N90-1047
Address Senior Professor, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba,
City Mumbai
Pin Code 400005
Country India
Gender Male
Specialization Ergodic Theory, Lie Groups, Probability measures on groups
Service in the Council Member, 2006-2008
Qualification PhD
Membership FASc, FNASc
  Award Srinivasa Ramanujan Medal, 2010
INSA Medal for Young Scientists, 1976

  Year of Election 1990  
E-mail dani@math.tifr.res.in
Personal Website

Shrikrishna Gopalrao Dani obtained his BSc and MSc degrees from the University of Mumbai. He then joined the Tata Institute of Fundamental Research (TIFR), Mumbai (1969) to work under the guidance of MS Raghunathan for his PhD degree, awarded by the University of Mumbai. He continued to be with TIFR and held visiting positions at various institutions including the Institute for Advanced Study, Princeton (1976-77 and 1983-84); Yale University, New Haven (1977-78); University of California, Berkeley (1982); Sonderfoschungsbereich-170, Goettingen (1990-91); University of Chicago (1992); Isaac Newton Institute, Cambridge (2000); and so on. In recent years, he has been a frequent visitor to the University of Rennes-1, and University of the Mediterranean, Marseille.

Academic and Research Achievements: Dani has contributed to two major themes: (i) study of flows on homogeneous spaces of Lie groups and their applications to Diophantine approximation, and (ii) probability measures on Lie groups. His work on the behaviour of orbits of flows on homogeneous spaces, with regard to their closures, distribution, recurrence, boundedness, divergence etc., and the applications of these aspects to questions in Diophantine approximation have had a major impact in the theory. His results on uniform recurrence of trajectories of unipotent flows played an important role in Ratner's proof of Raghunathan conjecture. Jointly with GA Margulis, Dani made significant improvements in Ratner's uniform distribution theorem and deduced a quantitative version of the Oppenheim conjecture. He has also been interested in extending the perspectives in classical probability theory to probability measures on more general locally compact groups, especially Lie groups. In this area he has obtained, together with his collaborators, notable results on the question of embedding infinitely divisible probability measures in continuous one-parameter convolution semigroups. He has published several expository articles and reviews on these topics.

Other Contributions: Dani served as an Editor of the Proceedings of Indian Academy Sciences (Mathematical Sciences). He has been a Member of the National Board for Higher Mathematics (since 1996); its Chairman (since 2006); and has also been a Member of the Commission for Development and Exchange of the International Mathematical Union (since 2002). He was elected President of the Commission for the term 2006-10. He has served as Council Member of Indian Academy of Sciences, Bangalore (1998-2000) and has been a Council Member of INSA (2006-08).

Awards and Honours: Professor Dani received several award and honours that include SS Bhatnagar Prize (1990), TWAS prize in Mathematics by the Academy of Sciences for the Developing World (2007), Fellow, Indian Academy of Sciences, Bangalore (1985), Fellow, National Academy of Sciences (India), Allahabad (1995), Invited Lecture at the International Congress of Mathematicians, Zurich (1994).

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