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Abstract
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In this talk, I will discuss the proof of a degree version of the celebrated Erd\H os-Ko-Rado theorem: given $n>2k$, for every intersecting $k$-uniform hypergraph $H$ on $n$ vertices, there exists a vertex that lies on at most $\binom{n-2}{k-2}$ edges. A degree version of the Hilton-Milner theorem was also proved for sufficiently large $n$.
The talk is based on joint works with Peter Frankl, Jie Han and Yi Zhao.
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