Member, the Academia Europaea

Fellow, the European Academy of Sciences

Fellow, the American Association for the Advancement of Science (AAAS)

Verne M. Willaman Professor of Mathematics

Fellow, inaugural class, American Mathematical Society (AMS)

2011 SIAM Fellow (see Penn State Science)

Francis R. and Helen M. Pentz Professor of Science

Invited speaker, ICM 2010

Ten breakthroughs in computational science by DOE

Invited speaker, ICIAM 2007

Humboldt Award, 2005

Top 25 Highly Cited Institutions and Authors in Mathematics, 1991–2001