She became researcher at the CNR institute IMATI (Istituto di Matematica Applicata e Tecnologie Informatiche) in 2001, research director in 2004 (on leave since 2016), and she is professor at Ecole Polytehcnique Federale de Lausanne since September 2016. From 2013 to 2016 she was the director of the IMATI.
She has been a visiting scholar at many institutions, including the Laboratoire Jacques-Louis Lions at the University of Paris VI, the École Polytechnique, the ETH Zürich, and the University of Texas at Austin (Institute for Computational Engineering and Sciences, ICES).
In 2007 A. Buffa was awarded the Bartolozzi Prize and in 2015 the Collatz Prize "for her spectacular use of deep and sophisticated mathematical concepts to obtain outstanding contributions to the development of computer simulations in science and industry" (Laudatio). Since 2017 she is member of the Academia Europea, and she is corresponding member of the Academia dei Lincei since 2018.
In 2008 she was invited (parallel) speaker at the EMS congress in Amsterdam, and 2014 she was an Invited (section) Speaker at the International Congress of Mathematicians in Seoul. In 2008 she received an ERC Starting Grant and in 2016 an ERC Advanced Grant.
