What type of details about thierry aubin  can be gathered from the following bio?  Bio: thierry aubin -lrb- 6 may 1942 -- 21 march 2009 -rrb- was a french mathematician who worked at the centre de mathématiques de jussieu , and was a leading expert on riemannian geometry and non-linear partial differential equations . his fundamental contributions to the theory of the yamabe equation led , in conjunction with results of trudinger and schoen , to a proof of the yamabe conjecture : every compact riemannian manifold can be conformally rescaled to produce a manifold of constant scalar curvature . along with yau , he also showed that kähler manifolds with negative first chern classes always admit kähler -- einstein metrics , a result closely related to the calabi conjecture . the latter result provides the largest class of known examples of compact einstein manifolds . aubin was a visiting scholar at the institute for advanced study in 1979 . he was elected to the académie des sciences in 2003 .

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