北京雁栖湖应用数学研究院 北京雁栖湖应用数学研究院

  • 关于我们
    • 院长致辞
    • 理事会
    • 协作机构
    • 参观来访
  • 人员
    • 管理层
    • 科研人员
    • 博士后
    • 来访学者
    • 行政团队
  • 学术研究
    • 研究团队
    • 公开课
    • 讨论班
  • 招生招聘
    • 教研人员
    • 博士后
    • 学生
  • 会议
    • 学术会议
    • 工作坊
    • 论坛
  • 学院生活
    • 住宿
    • 交通
    • 配套设施
    • 周边旅游
  • 新闻
    • 新闻动态
    • 通知公告
    • 资料下载
关于我们
院长致辞
理事会
协作机构
参观来访
人员
管理层
科研人员
博士后
来访学者
行政团队
学术研究
研究团队
公开课
讨论班
招生招聘
教研人员
博士后
学生
会议
学术会议
工作坊
论坛
学院生活
住宿
交通
配套设施
周边旅游
新闻
新闻动态
通知公告
资料下载
清华大学 "求真书院"
清华大学丘成桐数学科学中心
清华三亚国际数学论坛
上海数学与交叉学科研究院
BIMSA > Probabilistic Methods in Combinatorics \(ICBS\)
Probabilistic Methods in Combinatorics
The Probabilistic Method is a powerful tool for tackling many problems in discrete mathematics. It belongs to those areas of mathematics that have experienced the most impressive growth in the past few decades. Roughly speaking, its basic idea can be described as follows. In order to prove existence of a combinatorial structure with certain properties, we construct an appropriate probability space, and show that a randomly chosen element of this space has the desired property with positive probability.
This course provides a gentle introduction to the Probabilistic Method, with an emphasis on methodology. We will try to illustrate the main ideas by showing the application of probabilistic reasoning to various combinatorial problems.
讲师
本杰明·苏达科夫
日期
2023年09月21日 至 12月21日
位置
Weekday Time Venue Online ID Password
周四 15:30 - 17:20 Online ZOOM 03 242 742 6089 BIMSA
修课要求
It might be helpful to have basic knowledge of combinatorics and probability, but all relevant notions will be defined in the class.
课程大纲
The Basic Method: Ramsey numbers, Set-pairs with restricted intersections
Hypergraph 2-colouring, Tournaments with domination property

Linearity of Expectation: Sum-free subsets, Maximum cut in graphs
The maximum/minimum number of Hamilton cycles and Szele's conjecture

Permanents of Matrices: Minc's Conjecture
The maximum/minimum number of Hamilton cycles and Szele's conjecture

Method of Alterations: Graphs with large girth and large chromatic number
Recolouring and new bounds on non-2-colourable hypergraphs
Dependent random choice and its application to Ramsey and Turán-type problems

Second Moment Method: Turán's proof of the Hardy-Ramanujan theorem
Numbers with distinct sums, Random graphs and threshold functions
Cliques in random graphs

Large Deviations: Chernoff bounds, Consistent arcs in tournaments

Lovász Local Lemma: Proof of the local lemma, 2-colourability, cycles in directed graphs, colouring of integers with all shifts multicoloured

Correlation Inequalities: Four function theorem and a proof of the FKG inequality
Monotone properties in random graphs

Martingales: Chromatic number of random graphs
Isoperimetric inequality for the Hamming cube

Probabilistic Gems: Independence number of triangle-free graphs
Crossing numbers, incidence and additive number theory
听众
Advanced Undergraduate , Graduate
视频公开
公开
笔记公开
公开
语言
英文
讲师介绍
Benny Sudakov received his PhD from Tel Aviv University in 1999. He had appointments in Princeton University, the Institute for Advanced Studies and in University of California at Los Angeles. Sudakov is currently professor of mathematics in ETH, Zurich. He is the recipient of a Sloan Fellowship, NSF CAREER Award, Humboldt Research Award, is Fellow of the American Math. Society and was invited speaker at the 2010 International Congress of Mathematicians. He authored more than 300 scientific publications and is on the editorial board of 14 research journals. His main scientific interests are combinatorics and its applications to other areas of mathematics and computer science.
北京雁栖湖应用数学研究院
CONTACT

No. 544, Hefangkou Village Huaibei Town, Huairou District Beijing 101408

北京市怀柔区 河防口村544号
北京雁栖湖应用数学研究院 101408

Tel. 010-60661855
Email. administration@bimsa.cn

版权所有 © 北京雁栖湖应用数学研究院

京ICP备2022029550号-1

京公网安备11011602001060 京公网安备11011602001060