| 1983 | Rouse Ball lecture, Cambridge |
| 1987 | Bakerian Lecturer, Royal Society |
| 1988 | Elliott Montroll Memorial Lecture, Leiden |
| 1988 | Vikram Sarabhai lectures, Ahmedabad |
| 1989 | Loeb Lectures, Harvard |
| 1989 | Friday Evening Discourse, Royal Institution |
| 1989 | Racah Memorial Lecture, Weizmann Institute |
| 1989 | Margaret B Hays Lectures, Pittsburgh |
| 1991 | De Shalit Memorial Lecture, Weizmann Institute |
| 1991 | Segrè Memorial Lecture, Berkeley |
| 1992 | Feshbach Lectures, Massachusetts Institiute of Technology |
| 1992 | Fields Distinguished Lectures, Waterloo |
| 1992 | Sargent Lecture, Kingston |
| 1993 | Walker-Ames Lectures, Seattle |
| 1993 | S Town Stephenson Distinguished Lecture, Pullman. |
| 1993 | Schrödinger Lecture (Imperial College) |
| 1993 | President of physics section, British Association for the Advancement of Science |
| 1993 | Wood Memorial Lecture, Newcastle |
| 1994 | Racah Memorial lecture, Jerusalem |
| 1994-2000 | A D White visiting Professor-at-Large, Cornell University |
| 1995 | G C Steward Visiting Fellow, Gonville and Caius College (January-June) |
| 1995 | Child Health Christmas Lecture, Bristol |
| 1997 | Andrejewski Lectures, Berlin and Leipzig |
| 1997 | Joseph Ford Memorial Lecture, Atlanta |
| 1997 | Eliott Montroll Memorial Lectures, Rochester (New York) |
| 1997 | Founders day lecture, Inter-University Centre for Astronomy and Astrophysics, Pune |
| 1998 | Distinguished Visiting Professor, Texas A & M University |
| 1998 | Donegall Lectures, Trinity College Dublin |
| 1999 | First V L Shapiro Distinguished Lecture in Mathematics and Lawson Memorial Lecture in Physics, University of California at Riverside |
| 1999 | Forder lecturer, New Zealand and London Mathematical Societies |
| 1999 | Barut Memorial Lecture, Istanbul |
| 2000 | Friday Evening Discourse, Royal Institution |
| 2000 | W C Williams Lecture, Sheffield |
| 2000 | Hubert M James lecture, Purdue (Indiana) |
| 2000 | Eugene Feenberg lecture, Washington University of St Louis |
| 2002 | Josiah Willard Gibbs Lecture (American Mathematical Society), San Diego |
| 2002 | James Scott Prize Lecture (Royal Society of Edinburgh) |
| 2004 | Robert Cormack Lecture, Edinburgh |
| 2004 | J L Synge Memorial lecture, Dublin |
| 2005 | Simons Foundation Distinguished Lecture, State University of New York at Stony Brook |
| 2005 | Raymond and Beverley Sackler lecture, Copenhagen |
| 2005 | Rochester lecture, Durham |
| 2005 | Cochran Lecture, St John's College, Annapolis |
| 2006 | Fröhlich colloquium, Liverpool |
| 2006 | National Science Week Lecture, Norwich |
| 2006 | Sir Neville Mott Lecture, Loughborough |
| 2007 | John Lewis lecture, Birmingham |
| 2007 | Dirac Memorial Lecture, Cambridge |
| 2007 | Edward L Reiss Memorial lectures, Northwestern University, USA |
| 2007 | Kelvin memorial lecture, Glasgow |
| 2009 | Ramanujan Lecture, Saha Institute, Kolkata |
| 2009 | 50th Cherwell-Simon Memorial Lecture, Oxford |
| 2009 | 2009 Baylor Mathematics Lecture Series, Waco, Texas |
| 2009 | Plücker lecture, Bonn |
| 2010 | Primakoff lecture, University of Pennsylvania |
| 2010 | Sir Michael Atiyah Visiting Professor, Center for Advanced Mathematical Studies, American University, Beirut |
| 2011 | Princeton Center for Theoretical Sciences Inaugural lecturer and Hamilton Lecture, Princeton, USA |
| 2011 | Bernoulli Lecture, Groningen University |
| 2011 | First Marcos Moshinsky Lecture, Cuernavaca, Mexico |
| 2011 | Jentschke Lecture, DESY, Hamburg |
| 2012 | 10th C T Majumdar Memorial Lecture, S N Bose Institue, Kolkata |
| 2012 | Diamond Jubilee lecture, IIT Kharagpur |