Dániel Gerbner: The covering lemma and q-analogues of extremal set theory problems

zoom:  https://zoom.us/j/579532866?pwd=QkhMVTB6U1Bmb1prMW9VYzJXOUR2Zz09

We prove a lemma that generalizes Katona's cycle method. It is an extension of a lemma due to Holroyd and Talbot. It is based on the connection of the largest cardinalities (or weight) of structures satisfying some hereditary property and substructures satisfying the same hereditary property. We use it to show how results concerning forbidden subposet problems in the Boolean poset imply analogous results in the poset of subspaces of a finite vector space. 

https://arxiv.org/abs/1905.06994 

You can watch the lecture here: https://www.youtube.com/watch?v=5PscJaBDgLY