Peter studied Biochemistry and Theoretical Chemistry at the University of Vienna and Karolinska Institute. He did his Ph.D. in Computational Biochemistry with Amedeo Caflisch at the University of Zurich. After a short continuation as a postdoc in the same group, Peter joined the lab of Brian K. Shoichet at the University of California, San Francisco. This coincided with the publication of the structure of the first pharmacologically relevant G protein-coupled receptor, a unique opportunity to carry out one of the first studies of xray-structure-based ligand design for this protein class. From April 2011 until October 2016, he was an Emmy Noether Junior Group Leader at Philipps-University Marburg. Between May 2013 and April 2017, Peter was chairing COST Action CM1207 "GLISTEN: GPCR-Ligand Interactions, Structures, and Transmembrane Signalling: a European Research Network", which connected more than 210 scientists from 31 European countries.
Since October 2016, Peter is Professor of Pharmaceutical Chemistry, funded by the Heisenberg programme of the German Research Foundation DFG. His research interests focus on computational approaches to drug design, particularly tailoring properties of candidate drugs at an early stage.