Thierry Bouche’s Home Page

My research is focused on the study of hermitian vector bundles over complex analytic manifolds, specifically their sections and cohomology. After a few papers in the field, I have presented a synthesis of the methods I had to adapt or develop to succeed in the paper describing “the heat kernel approach” (now published by de Gruyter in a congress on “Higher dimensional complex variables”). You can also look at “2 vanishing theorems for vector bundles of mixed sign curvatures” for related results (published in Math Zeitschrift).

Another subject of interest is Arakelov theory such as developped by H. Gillet, Ch. Soulé or L. Szpiro: I have published with A. Abbes a new elementary and straightforward proof of the arithmetic Riemann-Roch theorem formerly due to Gillet and Soulé

If you read French, you could also be interested by these short & fast lecture notes I delivered during summer 1996 at a school in complex analysis. It is an introduction to differential calculus & geometry with special emphasis on applications to complex analysis (boundary Neumann problems & the like).

Here is my publications’ list.

December 20, 2006,
Thierry Bouche