# Mathematics Colloquia and Seminars

In a given permutation, an element is a peak if it is larger than the numbers next to it. For instance, the permutation 1432 has a peak (only) in the second position. This talk investigates the question: How many permutations in $S_n$ have peaks at a prescribed set of positions? We introduce this notion and discuss the resolution of an open problem of Billey, Burdzy and Sagan. We then discuss extensions of this work. This was joint work with Alex Diaz-Lopez, Pamela Harris and Erik Insko.