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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Gibbons' conjecture and Liouville theorem for master equations
主方程 Gibbons猜想 Liouville定理
2023/11/29
In this talk, we will discuss some of our recent work on the master equation involving the fully fractional heat operator. Specifically, we will present two main results. The first one pertains to a g...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Positivity and model complete fields
正性 模型完备域 有理数域
2023/11/13
In recent work with Will Johnson, we have shown that given a curve C over the rational number field Q with genus at least 2 and C(Q) is empty, the class of fields K of characteristic 0 such that C(K) ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：P-adic Simpson correspondence via exponential twisting
指数扭曲 P—adic—Simpson对应 p-adic-Simpson对应关系
2023/12/11
In this talk, I shall explain the work of G. Faltings on a p-adic Simpson correspondence, using exponential twisting. This reinterpretation of the correspondence makes clearer analogy between the p-ad...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Ambartzumian combinatorial formula and its applications
Ambartzumian 组合公式 有限线段集
2023/11/6
Consider a finite set of segments on a plane with endpoints in the general position. In [1] Sylvester posted a problem of finding the measure of the set of lines intersecting all of this segments. In ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Introduction to Allard’s regularity theorem（II）
阿拉德 正则性定理 导论
2023/5/17
We continue to discuss the proof of the Allard regularity theorem. In the second presentation, we will focus on the harmonic approximation and the iteration argument for getting the decay of the tilt-...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Introduction to Allard’s regularity theorem（I）
阿拉德 正则性 定理 导论
2023/5/10
In this short seminar, we will discuss the proof of the Allard regularity theorem, which is an $\epsilon$-regularity theorem for the mean curvature equation in the Geometric Measure Theory(GMT) settin...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Multiple solutions for semilinear subelliptic Dirichlet problem
半线性 次椭圆 狄利克雷问题 多种解
2023/4/27
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Multiple solutions for semilinear subelliptic Dirichlet problem。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Identities, inequalities and congruences for odd ranks and k-marked odd Durfee symbols
奇数秩 k标记 奇数杜菲符号 恒等式 不等式 全等
2023/4/23
In 2007, Andrews introduced the odd rank of odd Durfee symbols. Let N^0 (m,n) denote the number of odd Durfee symbols of n with odd rank m, and N^0 (r,m;n) be the number of odd Durfee symbols of n wit...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Supercongruences involving Motzkin numbers and central trinomial coefficients
莫茨金数 中心三项式系数 超同余
2023/4/21
In this talk, we investigate congruence properties for Motzkin numbers and central trinomial coefficients. Let M_n and T_n denote the nth Motzkin number and the nth central trinomial coefficient respe...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Borel—Wei—Bott theorem for Derived Flag Schemes
派生 标志方案 博雷尔-魏-博特定理
2023/4/13
The framework of derived algebraic geometry (DAG), developed by Toen-Vezzosi, Lurie and many others, allows us to extend Grothendieck’s theory of flag schemes of sheaves to the cases of complexes. In ...
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...