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School Colloquium——Stable reduction of algebraic curves and abelian varieties
北大 algebraic curves abelian varieties
2023/6/16
The stable reduction theorem was proved by Grothendieck for Abelian varieties and subsequently by Deligne and Mumford for projective curves.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the Riemann-Hilbert problem of confluent hypergeometric systems and Seiberg-Witten curves
超几何系统 塞伯格-维滕曲线 黎曼-希尔伯特问题
2023/4/21
This talk first solves explicitly a Riemann-Hilbert problem of confluent hypergeometric systems. It then conjectures and proves a special case that the WKB approximation of the monodromy data of confl...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rational points and homogeneous spaces over function fields of curves
曲线函数场 有理点 齐次空间
2023/4/17
In the last decade, there has been a growing interest in the study of rational points on homogeneous spaces of linear algebraic groups defined over fields having good arithmetical properties other tha...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Pseudorandomness of Sato-Tate Distributions for Elliptic Curves
椭圆曲线 佐藤-泰特分布 伪随机性
2023/4/13
Equidistribution is an important theme in number theory. The Sato-Tate conjecture, which was established by Richard Taylor et.al. in 2008, asserts that given an elliptic curve over Q without complex m...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Vanishing of some algebraic cycles on powers of Shimura curves
志村曲线 幂 代数 循环消失
2023/4/27
For a smooth projective variety over a number field, the Beilinson—Bloch conjecture predicts that Chow groups of algebraic cycles modulo rational equivalence can be determined using cohomological data...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Strong approximation and integral quadratic forms over affine curves
仿射曲线 强近似 积分二次形式
2023/5/9
Let $k$ be a field of characteristic 0 and let $C$ be the a smooth affine curve over $k$. We will first discuss applications of strong approximation to the theory of integral quadratic forms over $C$....
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Birkhoff genericity for points on curves in expanding horospheres and Diophantine applications
星座图 曲线 Birkhoff泛型 丢番图应用
2023/5/16
Let $\{a(t):t \in \mathbb{R}\}$ be a diagonalizable subgroup of $SL(d,\mathbb{R})$ for which the expanded horosphere $U$ is abelian. By the Birkhoff ergodic theorem, for any point $x \in SL(d,\mathbb{...