M. Chen a obtenu son doctorat de Stanford University en 1992. Il a depuis été professeur à l'institut Massachussetts de Technologie, à l'université Northwestern et à l'université de Californie. Ses travaux en analyse géométrique ont également été reconnus et il est ainsi devenu récipiendaire d'une bourse Alfred P. Sloan Research, du National Science Foundation. Il a publié une vingtaine d'articles et il est un conférencier invité partout à travers le monde, de la Chine à l'Angleterre aux États-Unis.

JINGYI CHEN (Université de Colombie Britannique) a donné sa conférence au CRM le 18 janvier 2002.

Mr. Chen obtained a Ph.D. from Stanford University in 1992. He has since been a professor at the Massachussetts Institute of Technology, at Northwestern University and the University of California. His works in geometric analysis have been recognized. He was awarded the Alfred P. Sloan Research Fellowship from the National Science Foundation. He has published over twenty articles and is an invited speaker all over the world.

JINGYI CHEN (University of British Columbia) delivered a lecture on January 18, 2002.

Résumé / Abstract

QUATERNIONIC MAPPINGS BETWEEN HYPERKAHLER MANIFOLDS
Quaternionic maps (Q-maps) between hyperkahler manifolds are quaternionic analogues of Cauchy-Riemann equations of maps between Kahler manifolds and they arise naturally in higher dimensional gauge theory. Q-maps between quaternion numbers are just solutions to Cauchy-Riemann-Fueter equations. The Q-maps are energy minimizers in their homotopy classes, hence harmonic. We will discuss a necessary and sufficient condition on when a Q-map becomes holomorphic w.r.t. some complex structures, and give examples of Q-maps which cannot be holomorphic. When the domain of Q-maps is real 4-dimensional, we will analyze the structure of the blow-up set of a sequence of Q-maps, and show that the singular set of a stationary Q-map is at most a 1-dimensional Hausdorff rectifiable set. We will also indicate possible applications of this compactness result.