Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, August 23, 2016.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      July 2016             August 2016           September 2016
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2       1  2  3  4  5  6                1  2  3
3  4  5  6  7  8  9    7  8  9 10 11 12 13    4  5  6  7  8  9 10
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24 25 26 27 28 29 30   28 29 30 31            25 26 27 28 29 30
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Tuesday, August 23, 2016

12:00 pm in 243 Altgeld Hall,Tuesday, August 23, 2016

#### Organizational meeting

Abstract: We will hold a brief organizational meeting, then head directly to lunch.

3:00 pm in 241 Altgeld Hall,Tuesday, August 23, 2016

#### The structure of large intersecting families

###### Alexandr Kostochka (Illinois Math)

Abstract: A collection of sets is intersecting if every two members have nonempty intersection. We describe the structure of intersecting families of $r$-sets of an $n$-set whose size is somewhat smaller than the maximum ${n-1 \choose r-1}$ given by the Erdős-Ko-Rado Theorem. This extends the Hilton-Milner theorem on nontrivial intersecting families and answers a recent question of Han and Kohayakawa for large $n$. In the case $r=3$ we describe the structure of all intersecting families with more than 10 edges. We also prove a stability result for the Erdős matching problem. Our short proofs are simple applications of the Delta-system method introduced and extensively used by Frankl since 1977. This is joint work with Dhruv Mubayi.

3:00 pm in 243 Altgeld Hall,Tuesday, August 23, 2016