明日学术报告

Speaker:

马宁，State University of New York at  Buffalo

Inviter:

王标

Title:

Nonsplitting of the Hilbert Exact  Sequence and the Principal Chebotarev Density Theorem

Language:

Chinese

Time & Venue:

2023.03.03 09:00-10:00 Zoom ID: 839  2782 7695 Password: 1728

Abstract:

Let $K/k$ be a finite Galois extension  of number fields, and let $H_K$ be the Hilbert class field of $K$. We find a  way to verify the nonsplitting of the short exact sequence
 $$1\\to Cl_K\\to \\Gal(H_K/k){\\to}\\Gal(K/k)\\to 1$$ by finite calculation. Our  method is based on the study of the principal version of the Chebotarev  density theorem, which represents the density of the prime ideals of $k$ that  factor into the product of principal prime ideals in $K$. We also find  explicit equations to express the principal density in terms of the  invariants of $K/k$. In particular, we prove that the group structure of the  ideal class group of $K$ can be determined by reading the principal densities.

Speaker:

陈绿洲博士，Purdue University

Title:

Topological optimization and the  stable commutator length

Language:

Chinese

Time & Venue:

2023.03.03 09:00-10:00 Zoom会议：876 1256 8518 密码：20230303

Abstract:

It is a relatively recent discovery in  geometric topology that optimization problems of certain topological  complexity are connected to important geometric and topological information.  One example is the Gromov-Thurstonnorm, which is the minimal complexity of  surfaces representing a given second homology class, and it is closely  related to fibrations of 3-manifolds as surface bundles. This is an  introductory talk on a relative version of the Gromov-Thurston norm called  the stable commutator length (scl), which is the minimal complexity of  surfaces bounding a given loop. I will explain its computation and sharp  lower bounds in relation tolinear programming, as well as its close relation  to various problems in topology and group theory.

Speaker:

李婵颖，中国科学院数学与系统科学研究院

Inviter:

中科院数学院学术报告会组委

Title:

轨道威胁自主规避决策与反馈机制

Language:

Chinese

Time & Venue:

2023.03.03 10:40-11:50 南楼204教室

Abstract:

从1957年人类第一次发射卫星进入太空，空间目标总数达千万总质量达万吨。太空竞争加剧导致轨道空间日益拥挤, 碰撞风险激增且袭扰增多, 给航天器安全运行带来严峻挑战。报告将探讨太空环境的复杂、动态和不确定性给轨道威胁自主规避决策带来的一些控制问题和数学挑战。

Speaker:

张吉烈

Title:

重载列车分布式异步协同制动控制技术

Language:

Chinese

Time & Venue:

2023.03.03 20:00-21:00 腾讯会议：124-284-646

Abstract:

ECP重载列车分散式制动控制主要研究具有电气制动系统（ECP）的长大货运列车在制动过程中如何减小纵向冲动的控制问题。由于重载列车车厢之间存在车钩力，整个列车动态模型存在耦合作用，导致分布式控制器设计难以实现。目前大多方法还集中在列车整体设计方案的研究中。而分布式异步制动设计是我们研究的动力和目标。分布式异步设计将会对列车制动控制带来巨大改变，优势极为明显，如：减少计算量和计算速度，降低信号带宽，可靠性强，对车辆载重和运行工况自适应，提高载重和速度等优点。

Speaker:

李长喜，北京大学

Inviter:

张潇博士后

Title:

随机逻辑网络的建模与分析

Language:

Chinese

Time & Venue:

2023.03.03 09:30-11:30 思源楼425

Abstract:

随机逻辑网络是一类特殊的逻辑网络，由于随机性的存在，使其无法利用代数状态方法建模为齐次马尔科夫链。如何分析与控制随机逻辑网络是本领域的研究难点。本报告讲回顾逻辑网络的几类基本模型，给出经典模型可以建模为齐次马氏链的严格数学解释，同时建立分析与控制随机逻辑网络的一般框架。