2021年數(shù)學(xué)展望論壇日程安排

時間：12月4號

線下地點：kaiyun開云官方網(wǎng)站犀浦校區(qū)3號教學(xué)樓X30456

騰訊會議ID：652368231

題目：Visions of Automated Reasoning

報告人：Geoff Sutcliffe 美國邁阿密大學(xué)

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.

個人簡介：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).

題目：Metric distribution function

報告人：王學(xué)欽 中國科學(xué)技術(shù)大學(xué)

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.

個人簡介：王學(xué)欽，中國科學(xué)技術(shù)大學(xué)管理學(xué)院教授。2003年畢業(yè)于紐約州立大學(xué)賓漢姆頓分校。他現(xiàn)擔(dān)任教育部高等學(xué)校統(tǒng)計學(xué)類專業(yè)教學(xué)指導(dǎo)委員會委員、統(tǒng)計學(xué)國際期刊《JASA》等的Associate Editor、高等教育出版社《Lecture Notes: Data Science, Statistics and Probability》系列叢書的副主編。

題目：Abelian Group-invariant Steiner Quadruple Systems

報告人：季利均 蘇州大學(xué)

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 $v$.

個人簡介：蘇州大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授,主要研究領(lǐng)域為組合設(shè)計與組合編碼。2015年獲國際組合數(shù)學(xué)與應(yīng)用學(xué)會（ICA）頒發(fā)的Hall獎，曾獲批“國家基金委優(yōu)秀青年科學(xué)基金”。

題目：Global well-posedness of coupled parabolic systems

報告人：徐潤章 哈爾濱工程大學(xué)

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.

個人簡介：哈爾濱工程大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授，博士生導(dǎo)師，“龍江學(xué)者”青年學(xué)者，黑龍江省數(shù)學(xué)會常務(wù)理事，黑龍江省青年學(xué)術(shù)骨干?！豆枮I工程大學(xué)學(xué)報》編委， Advances in Nonlinear Analysis 主編， Applied Numerical Mathematics編委， Boundary Value Problems 副主編; Electronic Research Archive (ERA), formally known as Electronic Research Announcements in Mathematical Sciences 編委；The Annals of the University of Craiova - Mathematics and Computer Science series 編委，Opuscula Mathematica編委，《中國工業(yè)與應(yīng)用數(shù)學(xué)會簡訊》編委。 The 10th-13th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory 學(xué)術(shù)委員會委員（Scientific Program Committee）；第十四屆-第十九屆，非線性偏微分方程暑期講習(xí)班暨學(xué)術(shù)會議組織 委員會委員；12th-13th Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences 組織委員會委員。

題目：On the geometry of irreversible metric spaces

報告人：趙唯, 華東理工大學(xué)

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.

個人簡介：趙唯, 華東理工大學(xué)kaiyun開云官方網(wǎng)站副教授, 主要研究Riemann-Finsler幾何和度量幾何，相關(guān)工作發(fā)表在《Journal de Mathématiques Pures et Appliquées》、《Transactions of the American Mathematical Society》、《Mathematische Zeitshrift》、《Canadian Journal of Mathematics》、《Journal of Geometric Analysis》等國際權(quán)威期刊上。