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Casey Tompkins, Extremal forbidden poset problems in Boolean and linear lattices
Tuesday, November 10, 2020 @ 4:30 PM - 5:30 PM KST
Extending the classical theorem of Sperner on the maximum size of an antichain in the Boolean lattice, Katona and Tarján introduced a general extremal function $La(n,P)$, defined to be the maximum size of a family of subsets of $[n]$ which does not contain a given poset $P$ among its containment relations. In this talk, I will discuss what is known about the behavior of $La(n,P)$ and its natural extension to the lattice of subspaces of a vector space over a finite field. In particular, I will highlight some recent joint work with Jimeng Xiao. Many open problems will also be discussed.