YMSC Number Theory Seminar

组织者 Organizer:徐斌,蔡立
时间 Time: 16:00 – 17:00, 2020-7-14
地点 Venue:线上

报告摘要 Abstract

Title: Modular regulator with Rogers-Zudilin method
Speaker: Weijia Wang (ENS Lyon)
Time: 2020-7-14, 16:00 – 17:00
Abstract: Let Y (N) be the modular curve of level N and E(N) be the universal elliptic curve over Y (N). Beilinson (1986) defined the Eisenstein symbol in the motivic cohomology of Ek(N) and the work of Deninger–Scholl (1989) shows the Petersson inner product of its regulator gives us special L-values. In this talk I will present how to relate the modular regulator with L-value of quasi-modular forms by using Lanphier’s formula and Rogers–Zudilin method. 
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Meeting ID: 916 5344 6007
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Title: Projective bundle theorem in MW-motives

Speaker: Nanjun Yang (YMSC, Tsinghua)
Time: 2020-7-2, 10:00 – 11:00
Abstract: We present a version of projective bundle theorem in MW-motives (resp. Chow-Witt rings), which says that $\widetilde{CH}^*(\mathbb{P}(E))$ is determined by $\widetilde{CH}^*(X)$ and $\widetilde{CH}^*(X\times\mathbb{P}^2)$ for smooth quasi-projective schemes $X$ and vector bundles $E$ over $X$ with odd rank. If the rank of $E$ is even, the theorem is still true under a new kind of orientability, which we call it by projective orientability. As an application, we compute the MW-motives of blow-ups over smooth centers. (arXiv 2006.11774)
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 Meeting ID: 916 5344 6007
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Title: Elliptic cocycle for GLN(Z) and Hecke operators

Speaker: Hao Zhang (Sorbonne Université)
Time: 2020-7-2, 16:00 – 17:00
Abstract: A classical result of Eichler, Shimura and Manin asserts that the map that assigns to a cusp form f its period polynomial r_f is a Hecke equivariant map. We propose a generalization of this result to a setting where r_f  is replaced by a family of rational function of N variables equipped with the action of GLN(Z). For this purpose, we develop a theory of Hecke operators for the elliptic cocycle recently introduced by Charollois.  In particular, when f is an eigenform, the corresponding rational function is also an eigenvector respect to Hecke operator for GLN. Finally, we give some examples for Eisenstein series and the Ramanujan Delta function.
Zoom https://zoom.us/j/91653446007?pwd=QUFEUTZramJNeGpBdjVSWUV6cmpBZz09
Meeting ID: 916 5344 6007
Password: 8Ma4ed