报告题目：Hypergraph Turan numbers vis Lagrangians

报告人：Jiang Tao  迈阿密大学

报告时间：12月23日  下午4点

地点：1518

摘要：In extremal problems for hypergraphs, one typically aims to 

find the extreme value of a hypergraph parameter subject

to some constraints. One primary example is the study of

the hypergraph Turan number ex(n,H) of a given hypergraph H,

which is defined to be the maximum number of hyperedges 

an n-vertex hypergraph G can have without containing H as

a subhypergraph. The hypergraph Turan problem is notoriously

difficult with very few known asymptotic or exact result.

Somewhat surprisingly a lot of success has been found 

in the study of hypergraph Turan numbers of so-called extensions,

in which asymptotic or even exact results can be established

via the study of the extreme value of another parameter of

hypergraphs G, called the Lagrangian of G.  Given a weight

assignment w of nonnegative reals to the vertices of G with sum 1,

the weight of hyperedge e is the product of weights of vertices contained

in e. The Lagrangian of G is the maximum total edge-weight over

all weight assignments on its vertices.

We survey recent exact hypergraph Turan results via the determination of Lagrangians.