Infinite combinatorics, definability, and maximal cofinitary groups


题目:Infinite combinatorics, definability, and maximal cofinitary groups

报告人:David Schrittesser(哈尔滨工业大学



Zoom会议会议号:832 6498 6834,会议密码:2023

摘要:The notion of a cofinitary groups was named by Peter Cameron in the 1980ies, as a dual to the notion of finitary permutation groups. Cameron asked about such groups which are maximal in the sense that they are not proper subgroups of another cofinitary group.

Presumably due to a superficial similarity with so-called MAD families, it was long thought that such maximal cofinitary groups are necessarily extremely complicated objects, akin to monsters like the paradoxical decomposition of the sphere. It turns out that on the contrary, they can be constructed in a very, very concrete manner.

In this talk, I will sketch some ideas leading to this construction and give a some context to explain why it surprised everyone. There are also some possible connections to the world of operator algebras which I will discuss if time permits.

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