报告一

报告题目：Percolation theory - A brief history（I）

主讲：Henry Liu（中山大学数学学院副教授）

时间：5月31日（周五）下午2:00-3:00

地点：南校区院系楼152会议室

主办单位：数学与统计学院

报告摘要：What happens when water is poured into a porous medium? How efficient is a coffee maker? These are some questions that can be addressed by the subject of percolation theory. The subject was founded by Broadbent and Hammersley in the mid 1950s, and has since attracted significant attention from experts in the fields of physics and mathematical analysis. Several deep results have been proved, and many more problems were proposed. An early spectacular result in percolation theory is that the critical probability for bond percolation on the square lattice is exactly 1/2, with the lower and upper bounds proved by Harris (1960) and Kesten (1980).

In this short course, we shall present some of the landmark achievements in percolation theory, as well as recent developments and results in the subject.

主讲人介绍：Henry Liu,中山大学数学学院副教授，本科和硕士毕业于英国University College London，美国Memphis大学博士，学习经历包括剑桥大学的高等数学研究中心,并先后在匈牙利Alfred Renyi Institute of Mathematics、西班牙Universitat Politecnica de Catalunya、英国University College London、葡萄牙Universidade Nova de Lisboa、中南大学从事博士后研究工作。师从国际著名数学家Béla Bollobás教授（培养出包括1998年菲尔茨奖获得者Timothy Gowers在内的多名国际著名数学家），研究兴趣包括极值图论、随机组合、代数图论以及超图等多个领域，在J. Graph Theory、SIAM Discrete Math.、Linear Algebra & its Applications等学科内国际主流SCI源期刊发表近30篇论文。

报告二

报告题目：Mantel's Theorem for Random Hypergraphs

主讲：胡平（中山大学数学学院副教授）

时间：5月31日（周五）下午3:00-4:00

地点：南校区院系楼152会议室

主办单位：数学与统计学院

报告摘要：A classical result in extremal graph theory is Mantel's Theorem, which states that every maximum triangle-free subgraph of $K_n$ is bipartite. A sparse version of Mantel's Theorem is that, for sufficiently large p, every maximum triangle-free subgraph of G(n,p) is w.h.p. bipartite. DeMarco and Kahn proved this for $p > K\sqrt{\log n/n}$ for some constant K, and apart from the value of the constant, this bound is best possible. We study an extremal problem of this type in random hypergraphs. Denote by $F_5$ the 3-uniform hypergraph with vertex set {a,b,c,d,e} and edge set {abc, ade, bde}. Frankl and Furedi proved that the maximum 3-uniform hypergraph on n vertices containing no copy of $F_5$ is tripartite for n>3000. A natural question is that for what p is every maximum $F_5$-free subhypergraph of $G^3(n,p)$ w.h.p. tripartite. We show this holds for p>K log n/n for some constant K and does not hold if $p=0.1\sqrt{\log n}/n$. Joint work with Jozsef Balogh, Jane Butterfield and John Lenz.

主讲人介绍：胡平，中山大学数学学院副教授，本科毕业于北京大学数学系，2014年8月在美国伊利诺伊大学香槟分校(University of Illinois at Urbana-Champaign)获得数学博士学位，2014年10月至2017年8月在英国华威大学(University of Warwick)任研究员(Research Fellow)，2017年入职中山大学任副教授。胡平一直从事组合数学领域中极值组合方向的科学研究，在领域内的Ramsey理论，Turan理论，染色问题等方向均有成果。目前论文均发表在图论领域的国际一流期刊上，其中在极值图论领域顶级期刊Journal of Combinatorial Theory, Series B发表论文三篇，Random Structures & Algorithms发表论文一篇，并在极值图论领域一流期刊Combinatorics, Probability and Computing发表论文两篇，Journal of Graph Theory发表论文一篇，European Journal of Combinatorics发表论文两篇。

数学与统计学院“前沿学术论坛”由广东外语外贸大学数学与统计学院发起创办，是数学统计学科高层次常态化学术交流平台。论坛不定期邀请国内外知名学者围绕数学统计国际前沿动态及热点研究领域展开交流与探讨，通过学术报告、学术沙龙、研讨会等形式为师生提供向国内外同行学习交流的机会，接触学术前沿，拓宽学术视野，激发学术热情，提升我校师生的创新能力。