报告题目：Jumping numbers or non-jumping numbers of hypergraphs 

报告人：彭岳建  湖南大学

报告时间：5月23日 4:30-5:30

地点：1218

摘要：

A number α ∈ [0,1) is jump for r-uniform graphs if there exists a constant c > 0 such that for any family F of r-uniform graphs, if the Turán density of F is greater than α, then the Tur′ an density of F is at least α + c. A fundamental result in extremal graph theory due to Erd¨ os and Stone implies that every number in [0,1) is a jump for r = 2. Erd¨ os also showed that every number in [0,r!r r ) is a jump for r ≥ 3. Furthermore, Frankl and R¨ odl showed the existence of non-jumps for r ≥ 3. But there are still a lot of unknowns regarding jumps or non-jumps for hypergraphs. We give a survey on the known result.