タイトル：Nonabelian Cohen Lenstra Heuristics
日時：2024/7/18
講演者：ウィリヤード 賢（イリノイ大学アーバナシャンペイン校 博士課程学生）
会場：武蔵野研究開発センタ
The Cohen-Lenstra heuristics provide conjectures on the distribution of class groups of quadratic number fields. We are a long way from proving these heuristics, but nevertheless the conjecture has been generalized in several different directions. A nonabelian version of the Cohen-Lenstra heuristics was first stated by Boston, Bush, and Hajir, which studied distributions of pro-p quotients of the Galois group of the maximal unramified extension of quadratic number fields. Later, Liu, Wood, and Zureick-Brown stated a conjecture replacing quadratic extensions with certain totally real Galois extensions. Evidence for these conjectures comes from analogous results for function fields, for which weaker versions of these conjectures have been proved. In this talk I will go through the history of these heuristics. I will also discuss a totally imaginary analogue of the conjectures of Liu, Wood, and Zureick-Brown, and an idea of the proof of a weak version of these conjectures in the function field case.