Date
Tue, 08 Nov 2016
14:30
Location
L6
Speaker
Liana Yepremyan
Organisation
Oxford University

The Turán number of an $r$-graph $G$, denoted by $ex(n,G)$, is the maximum number of edges in an $G$-free $r$-graph on $n$ vertices. The Turán density  of an $r$-graph $G$, denoted by $\pi(G)$, is the limit as $n$ tends to infinity of the maximum edge density of an $G$-free $r$-graph on $n$ vertices.

During this talk I will discuss a method, which we call  local stability method, that allows one to obtain exact Turán numbers from Turán density results. This method can be thought of as an extension of the classical stability method by  generically utilising the Lagrangian function. Using it, we obtained new hypergraph Turán numbers. In particular, we did so for a hypergraph called generalized triangle, for uniformities 5 and 6, which solved a conjecture of Frankl and Füredi from 1980's.

This is joint work with Sergey Norin.

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