Seminar
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Location: | Simons Institute for the Theory of Computing: Melvin Calvin Laboratory |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
This talk will address the questions "what is a random number?" and "what is a random permutation?" and make connections between the two seemingly dissimilar problems. I will describe how a certain Poisson model underlies both questions, from a factorization point of view, and how to use this to predict how the prime factors of typical integers and cycles of typical permutations are distributed. This has applications to interesting questions about divisors of integers, the familiar multiplication table, sets fixed by permutations, generation of the symmetric group, and other questions.