Event Type:

Number Theory Seminar

Date/Time:

Tuesday, November 30, 2021 - 10:00 to 10:50

Location:

ALS 0006

Local Speaker:

Abstract:

This is an expository talk on random partitions. This subject has gained popularity in the last 20 years with many precise results due to exact formulas arising from determinantal formulas, orthogonal polynomials, representation theory, etc. In this talk, I will focus on one particular, central and motivating example of random partitions; the Plancherel measure. For this measure, the weight of a partition in this measure is proportional to the dimension squared of the irreducible representation (of the symmetric group) labeled by the partition. It turns out that the Plancherel measure is related to the problem of the longest increasing subsequence of a uniformly random permutation; a problem originally posed by Ulam in 1961 and initially developed by Hammersley in 1972, and Vershik-Kerov and Logan-Shepp in 1977. This talk should be accessible to a wide audience with no background in probability or representation theory necessary.