##### Department of Mathematics,

University of California San Diego

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### Food For Thought

## Jason O'Neill

#### UCSD

## On the Union of Sets in Extremal Combinatorics

##### Abstract:

Given $s$ finite sets $A_1, \ldots, A_s$, determining the size of the union of the $s$ sets is an easy problem. Determining the maximimum number of size $k$ subsets of an $n$ element set for which there does not exist $s$ sets which union has size $q$ is a very hard problem in general. Many problems in extremal set theory can be restated in this language for particular choices of $s,k,q$. For instance, the case where $s=2$ is equivalent to the complete intersection theorem, and when $sk=q$, this is equivalent to the Erd{\H o}s matching conjecture; one of the biggest open problems in the field. This talk is based off a recent paper of Peter Frankl and Andrey Kupavskii.

### October 25, 2019

### 12:00 PM

### AP&M 5402

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