| • Berkovich analytic spaces, Huber analytic spaces and the global analytic spaces of Poineau. |
| • Stein spaces in complex and non-Archimedean geometry and related notions. |
| • Bornological algebraic structures and their use in geometry and functional analysis. |
| • Derived geometry in a broad sense, both algebraic and analytic. |
| • Exact categories and in particular quasi-Abelian categories. |
| • Geometry over the field with one element and its applications to arithmetic, to L-function theory and Langlands program. |
| • Homotopy theory and ∞-categories. |
| • Motives in algebraic and analytic geometry. |
| • Rigid cohomology and p-adic differential equations. |
