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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The Brauer-Manin obstruction on algebraic stacks
代数栈 Brauer-Manin阻塞 Hasse原理
2023/11/29
The Brauer-Manin obstruction is an old topic in local-global principle of varieties. I will talk about Brauer-Manin obstruction on algebraic stacks and extend some classical results such as the exact ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rooted trees, Hopf algebras and rough paths
有根树 Hopf代数 粗路径
2023/11/15
In this talk, we first recall some classical Hopf algebras on rooted trees, including Connes-Kreimer Hopf algebra and Loday-Ronco Hopf algebra. Then we give a combinatorial description of the coproduc...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Toric Algebras and Matroids
Toric代数 拟阵 复曲面代数
2023/11/13
In the first lecture I will give an introduction to toric algebras. A toric algebra can be seen as a monomial subalgebra, or as a quotient of a polynomial ring by a binomial prime ideal. We will discu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Integrability and constructions of the peakon systems
peakon系统 可积性 构造 Camassa-Holm方程
2023/11/13
Since the discovery of Camassa-Holm equation, because of the special properties that peakon gets, it has received considerable attention in modern Mathematics and Physics. Many new integrable dynamic ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rigidity results in mapping class groups and homeomorphism groups
映射类群 同胚群 刚性结果
2023/11/13
Mapping class groups and homeomorphism groups are symmetry groups of surfaces and all manifolds. They are usually very rigid, in the sense that their automorphism groups only consist of conjugation. I...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Top-heaviness of lower Bruhat intervals
较低 Bruhat区间 顶部厚重感
2023/11/13
Bjorner and Ekedahl (Ann. of math., 2008) proved that lower Bruhat intervals of crystallographic Coxeter groups are top-heavy using Hodge theory. Using Soergel bimodules and their Hodge theory establi...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Asymptotic log-concavity of dominant lower Bruhat intervals
显性 Bruhat区间 渐近对数凹性
2023/11/13
The unimodality of lower Bruhat intervals for the “upper half” remains as an open problem. For affine Weyl group W with corresponding finite Weyl group W_f, we prove that lower W_f-parabolic Bruhat in...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A link invariant from higher-dimensional Heegaard Floer homology
高维 Heegaard-Floer同调 链接不变量
2023/11/13
We define a higher-dimensional analogue of symplectic Khovanov homology. Consider the standard Lefschetz fibration of a 2n-dimensional Milnor fiber of the A_{k-1} singularity. We represent a link by a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Recent progress on holomorphic Morse inequalities
全纯 Morse不等式 CR流形
2023/11/13
In this talk, we present recent progress on holomorphic Morse inequalities. We first review the history and motivation. Then we introduce recent results on CR manifolds. Finally we give a uniform proo...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Characterizations of Separably Differentially Closed Fields
可分 微分闭域 微分场
2023/11/7
In this talk, we define a new class of differential fields called separably differentially closed fields and show their several characterizations by comparing them with differentially closed fields of...
Minicourse——Purity of Brauer groups: application of perfectoids
北大 Purity of Brauer groups application of perfectoids
2023/6/16
Grothendieck predicted that the cohomological Brauer group of a regular scheme X is insensitive to removing a closed subscheme Z of X of codimension>=2. By Gabber's several results, the conjecture was...
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：Morse boundaries of Groups
群 Morse边界 群论
2023/5/17
The Morse boundary of a proper geodesic metric space is a generalization of the Gromov boundary of a hyperbolic space. It is a quasi-isometry invariant to study "hyperbolic directions" in the space. T...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：两水平非正规因子设计的构造
两水平 非正规因子 设计 构造
2023/5/6
因子设计可分为正规设计和非正规设计，其中正规设计结构简单，试验次数被限制在2的幂次上。非正规设计结构复杂，但具有较为灵活的试验次数，并可用于估计更多的因子效应。作为一类特殊的非正规设计，平行平面设计受到了越来越多的关注。正规设计也被称为单平面设计，由来自同一家族的几个单平面行并置得到的设计被称为平行平面设计。由三个平行平面构成的平行平面设计是最常用的非正规设计。将其推广到具有f个平面的平行平面设计...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Projective measure without Projective Baire
投射贝尔 投射测量 勒贝格可测
2023/5/6
In this talk, I will give some of the context and a sketch of the proof of the following result which I proved a while ago: It is consistent (relative to a Mahlo catrdinal) that there is a projective ...