Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
The hypergraph container lemma is a powerful tool in probabilistic combinatorics that has found many applications since it was first proved a decade ago. Roughly speaking, it asserts that the family of independent sets of every uniform hypergraph can be covered by a small number of almost-independent sets, called containers.
In this talk, I will present two new versions of the hypergraph container lemma that utilise alternative notions of almost-independence, in place of the usual 'balanced supersaturation' property. The two lemmas display a number of other attractive features and have surprising connections to several other well-studied topics in probabilistic combinatorics.
This is joint work with Marcelo Campos (IMPA).