Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, May 11, 2021.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, May 11, 2021

2:00 pm in Zoom,Tuesday, May 11, 2021

#### VC-dimension: a perspective on conjectures of Erdos, Rado, and Schur

###### Janos Pach (Renyi Institute for Mathematics)

Abstract: According to the Erdos-Rado sunflower conjecture, for any integer $r>0$, there is a constant $c=c(r)>0$ such that any family of at least $c^k$ sets of size $k$ has $r$ members such that the intersection of every pair of them is the same. We come close to proving this conjecture for families of bounded Vapnik-Chervonenkis dimension. We use a similar approach to attack other Ramsey-type questions. Joint work with Jacob Fox and Andrew Suk.