Paul.Pollack

Affiliation: University of Georgia

Title Of Talk: How badly does unique factorization fail, normally?

URLS:
https://pollack.uga.edu/concentration_elasticity.pdf

Abstract: Let K be a number field, and let alpha be a nonzero, nonunit in O_K (the ring of integers of K). The elasticity of alpha, denoted rho(alpha), is defined as the largest ratio m/n, where m and n range over all possible lengths of factorizations of alpha into irreducible elements of O_K. It can be shown that the elasticities rho(alpha), as alpha ranges over O_K, cluster around a single constant depending only on K. This constant is most simply described in terms of optimal play in a game Enrique Treviņo and I call "group solitaire", with the group in question being the class group of K. This talk will describe these connections in detail and introduce results with Treviņo determining optimal play in group solitaire for two new families of groups.

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