Before joining LMH in 2007, I was Research Fellow at the Max Planck Institute for Mathematics in Bonn for one year. Prior to that I was a Heisenberg research fellow for five years, and associate professor in Konstanz (where I got my habilitation), Freiburg, Ulm and Philadelphia. I had extended research visits in Cambridge, Paris, Rennes, Lille, Copenhagen, Heidelberg, Tel Aviv, Jerusalem, Novosibirsk, Kyoto, Campinas, Rio de Janeiro, Saskatoon, Berkeley and Princeton. I was co-founder and fellow of the Freiburg Graduate School of Mathematical Logic and Applications (2002-2008, funded by the DFG, the German Research Foundation). I co-organised conferences in Oxford, Edinburgh, Freiburg, Konstanz, Oberwolfach and Luminy. I am a regular invitee to workshops at MFO Oberwolfach, CIRM Luminy and MSRI Berkeley. I was the Invited Speaker at the International Congress of Mathematicians (ICM), that took place in Rio de Janeiro in August 2018.
I am a member of the Mathematical Logic Group at the Mathematical Institute Oxford. My research interests are in logic, algebra and number theory. More specifically I have proved theorems on valuation theory, on model theory and on arithmetic of fields, on infinite Galois theory, on the Inverse Galois Problem, on Hilbert’s 10th Problem, on undecidability in number theory, on Grothendieck’s anabelian geometry and on profinite groups. You can watch two of my research talks in Luminy (2015) and at IHP Paris (2018).
At LMH I am tutoring all 1st and 2nd year undergraduates on algebraic topics (linear algebra, group theory, number theory etc.). In 2008 I launched the LMH Maths Seminar which brings together all mathematicians of the College (undergraduates, graduates, and tutors) once a term.
At the Mathematical Institute I regularly give lectures on Logic (Part B), Model Theory (Part C) and Valuation Theory (graduate lecture). I have also been running the Logic Seminar for many years.
I was Prelims Examiner for Paper I in 2015, 2016, and 2017.
I have taught graduate courses on Undecidability in Number Theory during summer schools in Cetraro and Oxford (both in 2012).