Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, April 01, 2014, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Shagnik Das

Supersaturation for Intersecting Families

A family of sets is said to be intersecting if it does not contain a pair of disjoint sets. The study of intersecting families is fundamental to extremal set theory, and the celebrated theorem of Erdős-Ko-Rado bounds the size of k-uniform intersecting families over [n].

A natural question to ask, an extension known as supersaturation, is how many disjoint pairs must appear in larger families. The study of supersaturation in this setting dates back to the late seventies, having attracted the attention of Ahlswede, Frankl, Katona and others. More recently, Katona, Katona and Katona introduced a probabilistic version of the supersaturation problem.

In this talk we shall present some recent results for both deterministic and probabilistic supersaturation, which provide partial solutions to conjectures of Bollobás-Leader and Kleitman-West.

This is joint work with Wenying Gan and Benny Sudakov.

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