Seminar: From Universal Discs to the Universal Grassmannian

On October 3, 2025, Christopher Brav will speak on 'From Universal Discs to the Universal Grassmannian'.

Abstract:
Sato's universal Grassmannian was introduced to give an algebro-geometric description of certain solutions of the KdV hierarchy in terms of a flow on this universal Grassmannian. Around the same time, Segal and Wilson introduced a more complex analytic analogue of the universal Grassmannian, and variations of the latter were also studied by Arbarello and de Concini, with applications to moduli spaces of curves and of principally polarized abelian varieties. In all cases, the relevant ambient space and subspaces are described in terms of functions on various kinds of discs. Using analytic geometry in the context of condensed mathematics, we introduce universal integral forms of the discs appearing in different approaches to the universal Grassmannian, and use this to give an integral form of the universal Grassmannian whose algebro-geometric specialization recovers the Grassmannian of Sato, whose complex analytic specialization recovers a thickening of Sato-Wilson or Arbarello-de Concini, and which also admits various non-archimedean specializations. This is joint work in progress with Yingdi Qin.

Time and place: 17:30, 6 Usacheva Ulitsa, Room 306