Speaker: Francesco lacca (L’Università di Firenze)
Time: 2025-06-25 14:00
Location: R1110, SIMIS
The aim of this talk is to discuss the basic theory of infinite-dimensional Grassmannian, which generalizes the classical version of the grassmannian manifold, and some relations with classical integrable systems, in particular KP hierarchy and some slight variation of it, and geometry. We will see how solutions of KP hierarchy come from tau-functions, which have nice geometric meaning, given by infinite grassmannian together with an action of GL(\infty). We will also give an interpretation of this in terms of fermions, which act on the section of dual determinant bundle on the grassmannian. After that, we will discuss the relation between elements of the grassmannian and algebraic curves with a chosen smooth point, and a formal coordinate around it.
Dr. lacca works in Condensed Mathematics, Derived Algebraic Geometry and Motivic Homotopy Theory.
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