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).