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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Local Method for Compositional Inverses of Permutation Polynomials
置换 多项式复合逆 局部方法
2023/4/18
In this talk, we will talk about a local method to find compositional inverses of all PPs, some new PPs and their compositional inverses are given.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Density of orbits and arithmetic degrees of automorphisms of projective threefolds
射影三重 轨道密度 自同构 算术度
2023/4/18
The Zariski dense orbit conjecture of the arithmetic dynamic is to study the existence of a rational point P with a Zariski dense orbit of a dominant rational self-map f of a projective variety X. Whe...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Higher dimensional Heegaard Floer homology and Hecke algebras
高维 希加德弗洛尔同调 赫克代数
2023/4/18
Higher dimensional Heegaard Floer homology (HDHF) is a higher dimensional analogue of Heegaard Floer homology in dimension three. It's partly used to study contact topology in higher dimensions. In a ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On Lehmer's problem
莱默问题 代数闭包 小Weil高度
2023/4/19
Let x be an algebraic number. Lehmer's problem predicts that the product of the degree of x and the Weil height of x is bounded by an absolute constant. The basic idea to tackle this problem is to stu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The de Rham cohomology in characteristic 0
特征0 德拉姆 上同调
2023/4/19
Discuss [Bha, §2.3-2.4]. See [Dri20, §1.3] for the notion of cones and quasi-ideals. Note that some of the remarks (e.g. Remark 2.2.15) [Bha, §2.2] may not have been covered in Lecture 1. Explain them...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Siegel Zeros and Applications
西格尔零点 Landau-Siegel零点 大黎曼猜想 狄利克雷L函数
2023/4/24
Siegel zeros are real zeros of L-functions that are very close to 1, the non-existence of which was conjectured as a direct consequence of the Grand Riemann Hypothesis (GRH). In this talk, we will sta...
Inductively approaching subsets by almost finite sets, we refute Scheepers’ conjecture under CH. More precisely, we prove the following.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：多重斜正交多项式和多分量pfaff格
多重 斜正交多项式 多分量 pfaff约束
2023/4/26
本报告将从pfaffian恒等式出发，讲述关于多分量pfaff格的发现，这其中包含了很多著名的经典可积方程，如DKP方程的贝克隆变换所对应的方程。之后，将从多分量pfaff格的解构造一族多重斜正交多项式。
带有少量非分裂纤维的纤维簇的有理点
非分裂纤维 纤维簇 有理点
2023/1/5
We revisit the abstract framework underlying the fibration method for producing rational points on the total space of fibrations over the projective line. By fine-tuning its dependence on external ari...
The first extended greatest common right divisor (GCRD) algorithm for parametric univariate polynomial matrices is presented. The starting point of this GCRD algorithm is the free property of submodul...
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：Berndtsson’s proof of the Bourgain-Milman theorem
伯恩松 布尔根-米尔曼定理 证明
2023/4/28
I will give a report on the Bourgain-Milman theorem. Berndtsson used complex methods to give a proof. I’ll talk about his papers. However, the best constant for the Bourgain-Milman theorem is still un...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：密码学中的数论计算问题
密码学 数论计算 代数数基
2023/5/5
本报告讨论几个密码学中常见的数论计算问题，包括模乘、模逆、椭圆曲线运算、和进制的代数数基表示等， 也涉及对其中一些问题的新的角度上的观察。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the subadditivity of generalized Kodaira dimensions (Part I)
广义 小平维度 子加性
2023/5/5
In these series of talks, we will focus on the study of the Iitaka conjecture, which predicts the subadditivity of Kodaira dimensions for any algebraic fiber space. In the first part, we recall some b...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The algebraic incarnations of the Artin Vanishing
Artin 消失 代数化身
2023/5/16
The non-abelian Hodge theory, briefly can be viewed as building a correspondence between certain topological objects, analytic objects, and algebraic objects. In this talk, I will show that Kodaira-ty...