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.
