An introduction to almost disjoint families

Sergio Garcia
Monday, November 12, 2019, 4:30pm-5:30pm
Ross N628

Hopefully in a few years, the Math Department will be moved to the brand new Cantor-Hilbert (CH) Building. There will be infinite many rooms in the 5th floor, 501, 502, 503, \dots Sadly all of them will be already occupied.

--No problem-- says the Office staff, we can find offices for the new grads. Your own office (no sharing). Furthermore, we can find room for the infinitely many students arriving in any of the infinitely many TTC trains (each one of those having infinitely many seats)

In this talk, we will discuss our favorite ways to solve this problem. Then, we will present almost disjoint families and some of the problems they are related with.

We say that an infinite subset A of the power set of the natural numbers is an almost disjoint family, if the intersection of any two distinct elements of A is finite. An almost disjoint family is mad (maximal almost disjoint), if it is not properly included in any larger almost disjoint family.

No set theory of topology knowledge is required, but there might be some highly non-trivial hand waving involved.