Sundqvist was educated at Uppsala University, where he received his PhD in Nuclear Physics. He was appointed professor of Ion physics in 1987, and elected rector magnificus in 1997, a position he resigned on 30 June 2006. He was president of the Association of Swedish Higher Education, a co-operative body for more than 40 institutions of higher education in Sweden, in 2005–2006.
He is a member of the Royal Swedish Academy of Sciences, and was the president of the academy from 1 July 2006 until 30 June 2009. He is also a member of the Royal Swedish Academy of Engineering Sciences, the Royal Society of Sciences in Uppsala, and the Royal Danish Academy of Sciences and Letters.
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- Press release from Uppsala University on Sundqvist's election to the Presidency of the Royal Swedish Academy of Sciences. (13 January 2006)