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Speaker: Mikos Bona (University of Florida)

Abstract: 

The theory of permutation patterns studies subsequences of permutations that behave in a prescribed way. It is a relatively young field that has seen tremendous progress in the last 30 years. In the first half of the talk, we will give an overview of the most important results and unsolved problems. Then we will discuss much more recent results.

One of them is a set of negative results, which provide some intutitive explanation as to why these problems are so difficult. Briefly, in most cases, we can prove that the relevant generating functions are not nice, even though we do not explicitly know what they are. The other family of questions is about a set of problems that have ”no right to be interesting” as they sound somewhat artificial, but provide extremely interesting numerical evidence, suggesting that there may be something interesting lurking below the surface after all.

The talk will be accessible to graduate students.