• 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. |