西南交通大学2021年数学展望论坛

2021年数学展望论坛日程安排

时间：12月4号

线下地点：西南交通大学犀浦校区3号教学楼X30456

腾讯会议ID：652368231

题目：Visions of Automated Reasoning

报告人：Geoff Sutcliffe 美国迈阿密大学

摘要：This talk celebrates the scientific discoveries and the service to the automated reasoning community of Lawrence (Larry) T. Wos, who passed away in August 2020. The talk covers Larry's most long-lasting ideasabout inference rules and search strategies for theorem proving, his work

on applications of theorem proving, and a collection of personal

memories and anecdotes that let us appreciate Larry's personality and

enthusiasm for automated reasoning.

个人简介：Geoff Sutcliffe is a Chair Professor of the Department of Computer Science at the University of Miami. He received a BSc(Hons) and MScfrom the University of Natal, and a PhD in Computer Science from the University of Western Australia. His research is in the area of Automated

Reasoning, particularly in the evaluation and effective use of automated reasoning systems. His most prominent achievements are: the first ever development of a heterogeneous parallel deduction system, leading to the development of the SSCPA automated reasoning system; the development and ongoing maintenance of the TPTP problem library, which is now the de

facto standard for testing classical logic automated reasoning systems;

the development and ongoing organization of the CADE ATP System

Competition - the world championship for classical logic automated

reasoning systems; and the specification of the TPTP language standards for automated reasoning tools. The research has been supported by grants from the National Science Foundation, the German Ministry for Research, the Australian Research Council, the European Union, and so on. The

research has produced over 130 refereed journal, conference,and workshop papers. He is an editor of Acta Informatica and the Formalised

Mathematics journal, and has been guest editor of several special

journal issues on topics in automated reasoning. He has contributed to

the automated reasoning and artificial intelligence communities as a

conference or program chair of (several instances of) the International Conference on Automated Deduction (CADE), the International Conference

on Logic for Programming Artificial Intelligence and Reasoning (LPAR),

and the International Florida Artificial Intelligence Research

Society (FLAIRS).

题目：Metric distribution function

报告人：王学钦 中国科学技术大学

摘要：Statistical inference aims to use observed samples to learn the

unknown properties of a population. It has become an integral step in

scientific reasoning. A building block of nonparametric statistical

inference is distribution function. The distribution function and

samples are connected to form a directed closed loop by the

correspondence theorem in measure theory and the Glivenko-Cantelli and

Donsker properties in statistics, and this connection creates a paradigm for statistical inference. However, existing distribution functions are defined in Euclidean spaces. Those distribution functions are no longer convenient to use or applicable in characterizing the rapidly evolving data objects of complex nature. Thus, it is imperative to develop the

concept of the distribution function in a more general space to meet

emerging needs. Note that the linearity allows us to use hypercubes to

define the distribution function in a Euclidean space, but without the

linearity in a metric space, we must work with the metric to investigate the probability measure. We introduce a class of novel quasi-distribution functions, or metric distribution functions, for metric space-valued random objects. We investigate the randomness of the data by the

distribution of metric between random object and a fixed location.

Working with the distribution of the metric in defining a probability

measure is particularly challenging. We overcome this challenge to prove the correspondence theorem and the Glivenko-Cantelli theorem for metric distribution functions in metric spaces that lie the foundation for

conducting rational statistical inference for metric space-valued data. Based on metric distribution function, we develop statistical methods

for homogeneity test, mutual independence test, and hierarchical

clustering for non-Euclidean random objects, and present comprehensive

empirical evidence to support the performance of our proposed methods.

个人简介：王学钦，中国科学技术大学管理学院教授。2003年毕业于纽约州立大学宾汉姆顿分校。他现担任教育部高等学校统计学类专业教学指导委员会委员、统计学国际期刊《JASA》等的Associate Editor、高等教育出版社《Lecture Notes: Data Science, Statistics and Probability》系列丛书的副主编。

题目：Abelian Group-invariant Steiner Quadruple Systems

报告人：季利均 苏州大学

摘要：Let $K$ be an abelian group of order $v$. A Steiner quadruple system of order $v$ (SQS$(v)$) $(K,\B)$ is called symmetric $K$-invariant if for each $B\in \B$, it holds that $B+x\in \B$ for each $x\in K$ and $B=-B+y$ for some $y\in K$. In this talk, we present that a symmetric $K$-invariant SQS$(v)$ exists if and only if $v\equiv 2,4 \pmod 6$, the order of each element of $K$ is not divisible by $8$ and there exists a symmetric cyclic SQS$(2p)$ for any odd prime divisor $p$ of $v$.

个人简介：苏州大学数学科学学院教授,主要研究领域为组合设计与组合编码。2015年获国际组合数学与应用学会（ICA）颁发的Hall奖，曾获批“国家基金委优秀青年科学基金”。

题目：Global well-posedness of coupled parabolic systems

报告人：徐润章 哈尔滨工程大学

摘要：The initial boundary value problem of a class of reaction-diffusion systems (coupled parabolic systems) with nonlinear coupled source terms is considered in order to classify the initial data for the global existence, finite time blowup and longtime decay of the solution. The whole study is conducted by considering three cases according to initial energy: low initial energy case, critical initial energy case and high initial energy case. For the low initial energy case and critical initial energy case the sufficient initial conditions of global existence, long time decay and finite time blowup are given to show a sharp-like condition. And for the high initial energy case the possibility of both global existence and finite time blowup is proved first, and then some sufficient initial conditions of finite time blowup and global existence are obtained respectively.

个人简介：哈尔滨工程大学数学科学学院教授，博士生导师，“龙江学者”青年学者，黑龙江省数学会常务理事，黑龙江省青年学术骨干。《哈尔滨工程大学学报》编委， Advances in Nonlinear Analysis 主编， Applied Numerical Mathematics编委， Boundary Value Problems 副主编; Electronic Research Archive (ERA), formally known as Electronic Research Announcements in Mathematical Sciences 编委；The Annals of the University of Craiova - Mathematics and Computer Science series 编委，Opuscula Mathematica编委，《中国工业与应用数学会简讯》编委。 The 10th-13th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory 学术委员会委员（Scientific Program Committee）；第十四届-第十九届，非线性偏微分方程暑期讲习班暨学术会议组织 委员会委员；12th-13th Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences 组织委员会委员。

题目：On the geometry of irreversible metric spaces

报告人：赵唯, 华东理工大学

摘要：In this talk, I will introduce the recent work joint with A. Kristaly concerned about the study of Gromov-Hausdorff convergence and stability of irreversible metric-measure spaces, both in the compact and noncompact cases. While the compact setting is mostly similar to the reversible case developed by J. Lott, K.-T. Sturm and C. Villani, the noncompact case provides various surprising phenomena. Since the reversibility of noncompact irreversible spaces might be infinite, it is motivated to introduce a suitable nondecreasing function that bounds the reversibility of larger and larger balls. By this approach, we are able to prove satisfactory convergence/stability results in a suitable -- reversibility depending -- Gromov-Hausdorff topology. A wide class of irreversible spaces is provided by Finsler manifolds, which serve to construct various model examples by pointing out genuine differences between the reversible and irreversible settings.

个人简介：赵唯, 华东理工大学数学学院副教授, 主要研究Riemann-Finsler几何和度量几何，相关工作发表在《Journal de Mathématiques Pures et Appliquées》、《Transactions of the American Mathematical Society》、《Mathematische Zeitshrift》、《Canadian Journal of Mathematics》、《Journal of Geometric Analysis》等国际权威期刊上。