Date:
Mon, 15/01/202414:30-15:30
Location:
Ross 70 and Zoom
Title: Symplectic Geometry and Selmer Spaces
Abstract: An effective approach to the Diophantine problem of enumerating all points on curves with non-abelian fundamental groups, such as those of genus greater than 1, is provided (conjecturally always) by the Chabauty-Kim method. The central object in this method is a Selmer scheme associated to the curve of interest and generalizing the association of Selmer groups to elliptic curves. In this talk, we'll show that arithmetic dualities produce (derived) symplectic and Lagrangian structures on associated spaces which reflect certain expectations coming from "arithmetic topology". This should be viewed as foundational towards a "TQFT" approach to L-functions and related invariants. This is joint work with Minhyong Kim.
Zoom link
https://huji.zoom.us/j/88037279712?pwd=N3MwWW5RYzRTZHg4K0U2bS80Rmxjdz09
Meeting ID: 880 3727 9712
Passcode: 955263
Abstract: An effective approach to the Diophantine problem of enumerating all points on curves with non-abelian fundamental groups, such as those of genus greater than 1, is provided (conjecturally always) by the Chabauty-Kim method. The central object in this method is a Selmer scheme associated to the curve of interest and generalizing the association of Selmer groups to elliptic curves. In this talk, we'll show that arithmetic dualities produce (derived) symplectic and Lagrangian structures on associated spaces which reflect certain expectations coming from "arithmetic topology". This should be viewed as foundational towards a "TQFT" approach to L-functions and related invariants. This is joint work with Minhyong Kim.
Zoom link
https://huji.zoom.us/j/88037279712?pwd=N3MwWW5RYzRTZHg4K0U2bS80Rmxjdz09
Meeting ID: 880 3727 9712
Passcode: 955263