Higher Siegel-Weil formula for the pair (GO(2), GSp(4)) and Modularity conjecture
Speaker: Đào Văn Thịnh (Viện Toán học)

Time: 9:30 - 11:00, September 28, 2022

Venue: Room 612, A6, Institute of Mathematics, VAST

Abstract: In this presentation, everything is over the function field. In the breakthrough works: "Shtukas and the Taylor expansion of L-functions I, II", Zhiwei Yun and Wei Zhang relate the derivative of L-function with the intersection theory on shtukas (more precisely, on moduli space of shtukas). Recently, with Tony Feng, they geometrized the higher Siegel-Weil formula for unitary groups in the sense that the derivative of the Siegel-Eisenstein series can be expressed in terms of the self-intersection of some special cycle in Shtukas. This may be viewed as a function-field analogue of the Kudla-Rapoport Conjecture. Moreover, they predict the modularity of the constructed cycle (Modularity conjecture). My purpose in this talk is twofold: the first is to introduce the Modularity conjecture, and the second is to present my attempt in proving this conjecture for the pair (GO(2), GSp(4)) .


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