Stars and their Discontents

Start: 09/10/2014 - 4:15pm
End  : 09/10/2014 - 5:15pm


Shahriar Shahriari, Pomona College


A collection of sets is called a star if they all have at least one element in common. A typical problem in extremal combinatorics, is to find the largest possible (or smallest possible) size of a collection that has some nice combinatorial property. Surprisingly often, the answer ends up being “the same size as an appropriate star except when it is not”. In this talk, we give a few examples of this phenomenon and then focus on the the Manickam–Mikl ́os–Singhi Conjectures for Sets and Vector Spaces. For twenty-five years, very little progress was made on these conjectures. But that changed this past year.

Freeburg Forum, Kravis Center (LC 62), Claremont McKenna College

Shahriari.pdf103.86 KB

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