时间：2026年6月16日（星期二）17:15-18:15
地点：西湖大学云谷校区E13-105
主讲人：Laurent Lafforgue, Lagrange Centre
报告题目：Computing with subspaces
报告摘要：Just as the classical notion of a space generalises to that of a Grothendieck topos, the classical notion of a subspace generalises to that of subtopos.
Subtoposes admit two equivalent types of concrete presentation: one in terms of Grothendieck topologies, the other in terms of axiom systems considered up to provable equivalence, according to a theorem by Caramello.
This dual equivalence makes it possible, in particular, to reformulate and study in topological terms all problems of provability in first-order geometric logic, and thus ultimately all problems of provability in mathematics.
Furthermore, the natural geometric operations on subspaces or subtopos define, via these equivalences, operations on topologies or on axiom systems that lend themselves to approximate calculations.
