• Berkovich, Huber analytic spaces and the global analytic spaces of Poineau. |

• Stein and compact 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 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. |

• Tropical geometry, its relations with analytic geometry and with mirror symmetry. |

• Homotopy theory and Ayoub motives in non-Archimedean Geometry. |

• Rigid cohomology and p-adic differential equations. |