2014: Invited Speaker, International Congress of Mathematicians, Seoul, South Korea

2010: Gold Medal, Royal Irish Academy

2009: Plenary Speaker, International Congress on Mathematical Physics, Prague, Czech Republic

2007-present: Member, Royal Irish Academy

1996-2000: Alfred P. Sloan Research Fellow, USA

1995-2002: DOE Outstanding Junior Investigator Award, OJI, USA

1995-2000: NSF CAREER Award (Presidential Young Investigator, PYI), USA
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2014-present: Visiting Professor, Simons Center for Geometry and Physics, Stony Brook, USA 

2014-2019: I. Gelfand Chair, Institut des Hautes Études Scientifiques, IHÈS, France

2003-2013: Louis Michel Chair, Institut des Hautes Ètudes Scientifiques, IHÈS, France 

2003-present: Director, the Hamilton Mathematics Institute TCD, Dublin, Ireland

2002-2008: Head, School of Mathematics, Trinity College Dublin, Ireland

2002-present: University Chair of Natural Philosophy (1847), Trinity College Dublin, Ireland 

1994-2002: Associate Professor, Yale University, Department of Physics, USA

1992-1995: School of Natural Sciences, Institute for Advanced Study, Princeton, USA 

1990-1992: Visiting Professor, Enrico Fermi Institute, University of Chicago, USA 

1987-2002: Leningrad Steklov Mathematics Institute, Leading Research  er, USSR 

1984-1987: Leningrad Nuclear Physics Institute, Research Scientist, USSR

1989: Doctor of Phys-Maths Sciences (second academic degree in USSR), Leningrad Steklov Mathematics Institute, USSR

1984: PhD (Candidate of Sciences), Leningrad University, Advisor - L. D. Faddeev