Gergő Gyenizse: The symmetric part of a finitely generated free lattice

We call a lattice term symmetric if any permutation of the
variables results in the same term. The symmetric terms (of a given
arity) form a sublattice in the free lattice (of that arity). In a
2018 paper, the author, together with Czédli and Kunos, proved some
surprising facts about this lattice, for example, that it is not
finitely generated. In this talk, I will show some new results about
this lattice. They naturally lead to the concept of medians, that is,
monotone majority operations, and inner medians, that is, majority
terms, of a lattice.