转载丨山东大学国际暑期课程《组合前沿》

山东大学国际暑期课程

《组合前沿》

授课时间及方式

授课时间：

8.1-8.6 (8: 30-11:30 am & 1:30-3:00 pm)

授课方式：

全英文线上授课

Zoom ID: 819 0982 4573

Password: 202208

课程简介

Part1. Introduction to expanders II

Jaehoon Kim (8:30-9:50 am)

Expanders are graphs whose all vertex sets have a large neighborhood. This simple-looking notion is important in many areas of mathematics and computer sciences. The expanders can be defined in a combinatorial way, a probabilistic way and an algebraic way. Last year, we saw interesting connections between them. This year, we will see more connections between expanders and other areas of mathematics and see how to construct good expanders.

Part2. Some topics in Algebraic/Topological Combinatorics

Jinha Kim & Minki Kim (10:00-11:30 am)

We will cover some results in algebraic/topological combinatorics, with focus on topological aspects of Helly's theorem. Topics we shall see include the nerve theorem, topological Hall theorem, topological Helly theorems, and some recently developed techniques such as applications of Knaster-Kuratowski-Mazurkiewicz lemma to geometric transversal problems.

Requirements: This course is intended for graduate students and advanced undergraduate students in mathematics, who have learned some basic knowledge in combinatorial/algebraic topology (simplicial complexes, homotopy, homology, Mayer-Vietoris sequence, etc).

Part3. Combinatorial Convexity

Hong Liu (1:30-3:00 pm)

We will study convexity space, an abstraction of the Euclidean convexity and see what properties, theorems can be generalised to such spaces. The particular ones that we will focus on are the interplay among, colorful/fractional Helly, Radon/Tverberg, Caratheodory, weak epsilon-net and (p,q)-properties.

授课教师简介

Jaehoon Kim

韩国韩国科学技术院(KAIST)助理教授，2014年于伊利诺伊大学香槟分校取得博士学位。主要从事图论、极值图论、图染色和超图方面的研究，与组合领域知名学者Kuhn和Osthus合作(2014ICM报告人)在Transaction of American Mathematical Society，Journal of European Mathematical Society，Journal of Combinatorial Theory Series B，Proceedings of the London Mathematical Society等国际著名杂志发表论文40余篇。

个人主页：

https://sites.google.com/view/jaehoon-kim

Jinha Kim

韩国基础科学研究所离散数学小组(IBS Discrete Mathematics Group (DIMAG))博士后研究员。主要从事拓扑组合、图论和离散几何的研究。在Proceedings of the American Mathematical Society，Journal of Combinatorial Theory Series A等国际著名杂志发表论文10余篇。

个人主页：

https://sites.google.com/view/jinhakim/home

Minki Kim

韩国光州科技大学(GIST)青年研究院。主要从事拓扑组合、图论和离散几何的研究。在Israel Journal of Mathematics， Proceedings of the American Mathematical Society，Journal of Combinatorial Theory Series A，等国际著名杂志发表论文10余篇。

个人主页：

https://dimag.ibs.re.kr/home/minkikim/

Hong Liu

韩国基础科学研究所(IBS)首席科学家、IBS极值组合与概率研究组组长。2015年于伊利诺伊大学香槟分校取得博士学位，后获得了享有盛誉的英国利弗休姆奖学金 (Leverhulme Early Career Fellowship)和欧盟的玛丽-居里奖学金(Marie Curie Individual Fellowship)。主要从事极值组合、概率组合、图论及其应用、离散几何、Ramsey理论、组合数论等方面的研究，在Forum of Mathematics, Pi，Journal of the European Mathematical Society，Proceedings of the London Mathematical Society，Discrete Analysis，Inthernational Mathematics Research Notice，Forum of Mathematics Sigma，Journal of Combinatorial Theory Series B及Combinatorica等杂志发表学术论文40篇，多次受邀在国际学术会议上作邀请报告。

个人主页：

https://www.ibs.re.kr/ecopro/hongliu/

           课程群：QQ群：794588327

联系人：

王光辉 [e-mail]

        常帆 [e-mail]

录屏地址：ECOPRO-SDU的个人空间_哔哩哔哩_bilibili往期暑期学校录屏地址：Combinatorics835的个人空间_哔哩哔哩_bilibiliSummer course：Methods in Combinatorics_哔哩哔哩_bilibili

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