2025年合肥工业大学数论研讨会
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会议信息
| 时间： | 2025年11月22日 |
| 地点： | 合肥工业大学翡翠湖校区翡翠科教楼B1710 |
| 主办单位： | 合肥工业大学数学学院 |
| 会务联系： | 张神星 zhangshenxing@hfut.edu.cn |
| 吴小胜 xswu@hfut.edu.cn |
报告安排
| 09:30-10:30 吕广世 (山东大学) Additive divisor problem for multiplicative functions We establish an asymptotic formula or a non-trivial upper bound for the additive divisor problem for multiplicative functions. Furthermore, we derive several applications to multiplicative functions in the automorphic context. In particular, our findings for a simple case resolve a question posed by Redmond in the 1970s. This work is a collaboration with Yujiao Jiang. |
| 10:40-11:40 丁一文 (北京大学) Filmax and Fil2nd-max Let 𝜌 be a 𝑛-dimensional de Rham representation of ℚ𝑝 of regular Hodge-Tate weights. I will first recall Breuil's conjecture on how to see Filmax of ∧𝑖DdR(𝜌), for 𝑖=1,…,𝑛−1, in a conjectural locally analytic representation of GL𝑛(ℚ𝑝) associated to 𝜌. Then I will discuss the existence of the extra locally algebraic constituents in the crystalline case, and how they are related with Fil2nd-max of ∧𝑖DdR(𝜌). This is a joint work with Christophe Breuil. |
| 14:30-15:30 申旭 (中国科学院晨兴数学中心) 𝑝-adic locally symmetric varieties We will discuss the theory of 𝑝-adic uniformization of Shimura varieties and some applications. More precisely, we will discuss a basic uniformization result for the Kisin-Pappas-Zhou integral models of Shimura varieties of abelian type, generalizing various known results in the literature. As applications, we obtain new cases of the compatibility between classical local L-parameters and the Fargues-Scholze parameters, and new cases of Fargues's eigensheaf conjecture. This is joint work in progress with Peihang Wu. |
| 15:40-16:40 舒杰 (同济大学) Arithmetic on Fermat curves The celebrated Fermat's last theorem, proved by A. Wiles, states that the Fermat equation 𝑋𝑝+𝑌𝑝=1 has no rational solutions with 𝑋𝑌≠0. We survey on various variants of Fermat-type problems and discuss a recent positive-density non-solubility result for twisted Fermat curves. This non-solubility builds on the distribution of Selmer ranks in twists of CM abelian varieties. |