Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, December 8, 2020.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    November 2020          December 2020           January 2021
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1  2  3  4  5  6  7          1  2  3  4  5                   1  2
8  9 10 11 12 13 14    6  7  8  9 10 11 12    3  4  5  6  7  8  9
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29 30                  27 28 29 30 31         24 25 26 27 28 29 30
31


Tuesday, December 8, 2020

2:00 pm in Zoom,Tuesday, December 8, 2020

#### The extremal number of Venn diagrams

###### Adam Zsolt Wagner (ETH Zurich)

Abstract: A cornerstone result of extremal combinatorics due to Sauer and Shelah bounds the size of a family in terms of its VC-dimension. In this talk we will make progress towards establishing a dual version of the Sauer-Shelah lemma, where the roles of points and sets are reversed. This is equivalent to asking how many sets can we take without creating a $k$-Venn diagram, i.e. $k$ sets with all $2^k$ regions of the form $B_1 \cap B_2 \cap ... \cap B_k$, where $B_i \in \{A_i , [n] - A_i\}$, are non-empty. We will solve the first interesting case by showing that a family without a $3$-Venn has size at most $O(n^3)$.

This is joint work with Peter Keevash, Imre Leader, and Jason Long.