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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Number of rational points of difference varieties in finite difference fields
有限差分域 差分簇 有理点数
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2023/4/13
A difference field is a field with a distinguished automorphism. Automorphisms of a finite field are powers of the Frobenius map. In this talk, I will discuss how to estimate the number of rational po...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Arithmetic purity of strong approximation for complete toric varieties
完整 复曲面品种 强近似 算术纯度
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2023/4/18
In this talk, I will discuss arithmetic purity of strong approximation : motivations and related results. Finally, for complete toric varieties, I will briefly explain my work on this topic.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Shimura varieties and p-adic geometry
志村变种 p-adic几何 代数几何空间 算术几何
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2023/4/28
Shimura varieties are a class of algebraic geometric spaces that play a very important role in arithmetic geometry, especially in the Langlands program. In recent years, methods from the geometric rep...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On varieties of general type with many global forms
全局形式 一般类型 品种
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2023/5/6
We expect that the study of pluricanonical systems of varieties of general type with many global forms can be reduced to the study of pluricanonical systems of varieties of lower dimensions. We show t...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some geometry of affine Deligne-Lusztig varieties
仿射 Deligne-Lusztig变种 几何
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2023/5/17
The mod p points of a Shimura variety have a conjectural description called the Langlands-Rapoport conjecture. In accordance with the conjecture, Rapoport defined (generalized) affine Deligne-Lusztig ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Special cycles on Shimura varieties and theta series
下村品种 θ系列 特殊循环
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2023/5/17
In this talk I will introduce special and generalized cycles on Shimura varieties and discuss how to use them to construct geometric and arithmetic theta series. Then I will briefly discuss the connec...