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Johannes Sjöstrand, Directeur de recherche émérite à l’IMB, a reçu le prix Bergman Prize 2018 – AMS

He is awarded the Bergman Prize for his fundamental work on the Bergman and Szego kernels, as well as for his numerous fundamental contributions to microlocal analysis, spectral theory, and partial differential equations (PDEs). He is especially being recognized for his groundbreaking work with L. Boutet de Monvel on describing the singularities and asymptotics of the Bergman and Szego kernels in strictly pseudoconvex domains in $C^n$. This work has been highly influential in subsequent developments on these and related topics. Sjostrand is also being recognized for his contributions to microlocal analysis, spectral theory, and PDEs. Together with A. Melin, he has developed the theory of Fourier integral operators with complex-valued phase functions, with applications to the oblique derivative problem. In joint work with R. B. Melrose, he has obtained fundamental results on the propagation of singularities for boundary value problems. Sjostrand has created the powerful and highly influential approach to analytic microlocal analysis, based on the theory of Fourier-Bros-Iagolnitzer (FBI) transforms and on the use of exponentially weighted spaces of holomorphic functions on the transform side. This approach was shown to be crucial in the study of regularity and propagation of singularities for PDEs (including boundary value problems) in the real analytic category. In joint work with B. Helffer, Sjostrand has developed an incisive and far-reaching analysis of the tunnel effect for semiclassical Schrodinger operators, including a study of the Witten complex, and has contributed significantly to the understanding of the fine spectral properties of the Harper operator. The work of Johannes Sjostrand in the theory of scattering resonances, including joint work with M. Zworski, has had a truly revolutionary impact on the subject. Among the many groundbreaking results obtained by Sjostrand in this direction, we mention a microlocal version of the method of complex scaling and a local trace formula for resonances. Sjostrand has given numerous decisive contributions to the spectral theory of non-self-adjoint operators, including operators of Kramers-Fokker-Planck type (joint work with F. Herau and C. Stolk) and analytic non-self-adjoint operators in dimension two (joint work with A. Melin and with M. Hitrik). More recently, Sjostrand has completed a deep and fundamental analysis of the Weyl asymptotics for the eigenvalues of non-self-adjoint differential operators in the presence of small random perturbations.

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