Combinatorial moment sequences

Analysis Seminar
Wednesday, April 5, 2023 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 005
Natasha Blitvic – Queen Mary University of London
Benjamin Jaye

We will look at a number of interesting examples — some proven, others merely conjectured — of Hamburger moment sequences in combinatorics. We will consider ways in which this positivity may be expected, for instance in different types of combinatorial statistics on perfect matchings that turn out to encode moments in noncommutative analogues of the classical Central Limit Theorem. We will also consider situations in which this positivity may be surprising, and where proving it would open up new approaches to a class of very hard open problems in combinatorics.