Recommendation letter for Mr. Alexandre Miguel de Araújo Lopes Mr. Alexandre Lopes has been since Febrary 2012 a PhD student in my Research group at the Univeristy of Freiburg. Its PhD will be finished by the end of Dezember 2015. As his supervisor I work together with him almost every day. In addition to his academic work, Mr. Lopes also works as a teaching assistant at the Institute of Physics. Besides that he is also the system administrator of our group. Mr. Lopes is an extraordinarily gifted scientist. His doctoral project combines methods and problems from extremely different areas (Geometry, Quantum Physics and Quantum Chemistry). He has, in all of these fields, quickly, autonomously and thoroughly worked and obtained considerable results. Even before the end of his PhD he has published partial results in internationally renowned peer-reviewed journals and presented them in conferences. As a group member, Mr. Lopes shows a big autonomy, responsibility and initiative. He assumes voluntarily more tasks inside of the group than he has to and reliably performs them. In particularly he administers the PCs, the network and the Linux server of the group (which is composed of 7 group members). His commitment to his teaching has been praised by other professors of the institute. Extraordinary is the almost native level of his English language skills both written and spoken. Although some of my employees (and myself as well) have lived several years in English speaking countries, Mr. Lopes excels all of us in this regard. Mr. Lopes is calm, modest and full of humor and he is highly regarded in my group. I deeply regret that I will lose Mr. Lopes. I would like to strongly recommend him to all possible employers. Best regards, David Gross