- Senior Research Fellow, All Souls College (from 2015 to 2017)
 
	- Professor of Mathematics, University of Oxford (from 2015 to 2017)
 
	- Professor, University of California at Berkeley (from 2006 to 2015)
 
	- Professor, University of Edinburgh (2007)
 
	- College Lecturer, St John’s College and Lecturer (2001-3) and Reader (2003–6), University of Cambridge (from 2001 to 2006)
 
	- Assistant Professor of Mathematics, University of Texas at Austin (from 1999 to 2001)
 
	- Research Fellow, St John’s College, Cambridge (from 1995 to 1998)
 
	- Szegö Assistant Professor (1994-1996) and NSF Postdoctoral Fellow (1996-9), Stanford University (from 1994 to 1999)
 
	- Postgraduate, Harvard and Cambridge Universities (from 1991 to 1994)
 
	- Undergraduate, Harvard University (from 1987 to 1991)
 
 
           
       
       
          
            
          
          
              
	- Topology
 
	- Group representations
 
	- Mathematical physics
 
 
           
       
       
          
            
          
          
              
	- (with D.S. Freed), ‘Relative quantum field theory’, Commun. Math. Physics 326 (2014), 459–476.
 
	- (with E. Frenkel), ‘Geometric Langlands correspondence near opers’, J. Ramanujan Math. Soc. 28A (2013), 123–147.
 
	- (with D.S. Freed and M.J. Hopkins), ‘Loop groups and twisted K-theory II’, J. Amer. Math. Soc. 26 (2013), 595–644.
 
	- ‘The structure of semi-simple 2D field theories’, Invent. Math. 188 (2012), 525–88.
 
	- (with D.S. Freed and M.J. Hopkins), ‘Loop groups and twisted K-theory III’, Ann. Math. 174 (2011), 947–1007.
 
	- (with C.T. Woodward), ‘The index formula on the moduli of G-bundles over a curve’, Ann. Math. 170 (2009), 495–527.
 
 
           
       
       
          
          
          
            
          
          
              
	- LMS Senior Berwick Prize (with D. Freed and M. Hopkins), 2014.
 
	- London Mathematical Society Whitehead Prize, 2002.
 
	- US National Science Foundation research grants (University of Texas at Austin, 2000–2002, University of California at Berkeley, 2007–present).