2023复旦大学数理逻辑暑期学校开始报名了！

VOL.2586

2023 Summer

2023年是复旦大学数理逻辑暑期学校的第六年，也是疫情后暑校第一年线下举办。今年，我们非常荣幸地邀请到了Renling Jin(金人麟)教授和Rizos Sklinos助理教授为我们带来精彩课程。

以下是本次暑校的详细介绍，同时附有注册报名通道，欢迎大家前来参与。

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授课教师

金人麟

金人麟，美国查尔斯顿学院（College of Charleston）数学系教授。主要研究兴趣包括非标准分析, 加法组合数论(additive-combinatorial number theory), 集合论, 模型论, 测度论, 一般拓扑学。曾在Journal of Symbolic Logic, Advances in Mathematics, The Transactions of American Mathematical Society等权威期刊发表多篇论文。

Rizos Sklinos

Rizos Sklinos，中国科学院数学与系统科学研究院数学研究所助理教授。

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报名申请

复旦大学数理逻辑暑期学校欢迎对数理逻辑有兴趣的在校本科生、研究生参加。

申请人须在请在5月31日23:59前完成以下报名步骤：

1.进入暑期学校官网填写在线报名申请：

http://logic.fudan.edu.cn/event2023/summer（或点击“阅读原文”）；

2.暑校不包食宿。如需申请经济补助（每人3000元，资助十人），请在填写好在线报名表的基础上，邀请一名推荐人从推荐人本人邮箱发送推荐信至[e-mail]。推荐人以数理逻辑及相关专业学者为佳。

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时间地点

时间

7月31日

~ 8月11日

地点

中国上海

复旦大学邯郸校区

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课程介绍

Some model theory of nonabelian free groups

Rizos Sklinos

In 1946 Tarski asked whether nonabelian free groups share the same first-order theory. Despite the fact that free groups were a well studied class of groups and techniques from different disciplines of mathematics have been developed to understand them, Tarski’s question proved very hard to tackle. It was only after more than fifty years, in 2001, that Sela and Kharlampovich-Myasnikov answered the question in the positive. Both works were voluminous and still to this day have not been fully absorbed by the mathematical community. It is worth mentioning that the tools developed allowed Sela to understand, model theoretically, also the class of torsion-free hyperbolic groups.

Surprisingly this common first-order theory has been proved, by Sela, to be stable. This is considered by many one of the most profound result in the model theory of groups.

In this mini-course we will explore what is model theoretically known about nonabelian free groups and more generally torsion-free hyperbolic groups. We will first give a mild introduction to both hyperbolic groups and stability theory and then develop all the adequate tools to explore this demanding topic that lies in the intersection of model theory with geometric group theory.

More precisely, we plan to show that the first-order theory of non abelian free groups is connected, unsuperstable and non-equational. It is not AE axiomatizable and only has QE down to boolean combinations of AE formulas. In addition, it does not have elimination of imaginaries, but one can add some easily understood families over which it has. Moreover, we will show that free groups are homogeneous, yet most surface groups are not. Using homogeneity we will understand forking independence in these standard models through JSJ decompositions (a tool of geometric group theory) and prove that this theory is ample. Finally we will show that no infinite field is interpretable in nonabelian free groups. The above list of results is not exhaustive, but mostly indicative of the topics we will touch on.

Nonstandard Analysis and Combinatorial Number Theory

金人麟 Jin Renling

The course is for the students with some knowledge on mathematical logic such as having had one-semester undergraduate level course on mathematical logic. In the first two days, we will cover basic ideas, concepts, properties, principles, etc. in nonstandard analysis. In the last two days, we will focus on applications of nonstandard methods to the problems in combinatorial number theory.

Program:

Day 1: First-order logic and ultrapower of superstructure

Day 2: Properties, principles, Loeb spaces and an application to finance

Day 3: Break

Day 4: Easy applications to combinatorial number theory

Day 5: Sophisticated applications to combinatorial number theory

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日程安排

课时1:  9:00 am - 10:15 am (GMT+8)

课时2: 10:45 am - 12:00 pm (GMT+8)

讨论:  14:00 pm - 16:00 pm (GMT+8)

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说明

申请人可通过点击阅读原文填写在线报名表

2023复旦大学数理逻辑暑期学校由复旦大学教务处主办，复旦大学哲学学院逻辑学教研室承办。

如有任何疑问，欢迎发送邮件至[e-mail]咨询。

转载自“FudanLogic”公众号

编辑 | 项湛雅

责任编辑丨汤克凤 隋艺菲