Present                     Editorial Boards, Editor, American Journal of Mathematics

2007 - present            Editors-in-Chief, Communications in Number Theory and Physics

2005 - present            Editors-in-Chief, Pure and Applied Mathematics Quarterly

2004 - present            Editor-in-Chief, Dynamics of Partial Differential Equations

2001 - present            Honorary Editor, Communications in Information and Systems 

1997 -                         Editorial Boards, Editor, Journal of Mathematical Physics

1997 - present            Editor-in-Chief, Advances in Theoretical Mathematics and Physics 

1997 - present            Editor-in-Chief, Asian Journal of Mathematics

1994 - present            Editor-in-Chief, Methods and Application of Analysis

1994 -                         Editorial Boards, Editor, Advances in Mathematics

1993 - present            Editorial Boards, Editor, Mathematical Research Letters

1993 - present            Editorial Boards, Advisor, Communications in Analysis and Geometry 

1993 - present            Editorial Boards, Advisor, Methods and Applications of Analysis

1982 - 1999                Editor, Communication in Mathematical Physics

1981 - 1988                Editor, Inventiones Mathematicae 

1980 - present            Editor-in-Chief, Journal of Differential Geometry