Complexity of the isomorphism relation
for Borel classes of non
Archimedean groups
报告专家：André Nies 教授（The University of Auckland）
报告时间：10月5日（周一）9:00-11:00
报告地点：数学学院东203
报告摘要：
Kechris, the speaker and Tent (The complexity of topological group isomorphism, JSL 2018) started the programme to determine the Borel complexity of the isomorphism relation for natural Borel classes of closed subgroups of Sym(N). The talk will report on progress.
For oligomorphic groups, the isomorphism relation is essentially countable by a 2021 result of Schlicht, Tent and the speaker. It remains open whether it is in fact smooth; only for certain natural subclasses smoothness is known. More recent work with Gao and Paolini shows that the isomorphism relation for pro-countable nilpotent-2 groups reduces $\ell_\infty$, and hence is not below graph isomorphism (arXiv:2512.12256). Whether it is complete for analytic equivalence relations remains open.
专家简介：
Professor André Nies is a Professor at the University of Auckland. His research interests include computability theory, algorithmic randomness, effective descriptive set theory, and logical aspects of algebraic and topological structures. He is a Fellow of the Royal Society of New Zealand, a recipient of the Humboldt Research Award, and was an invited speaker in the logic section of the 2010 International Congress of Mathematicians (ICM). He is the author of the monograph Computability and Randomness, published by Oxford University Press, and his research has appeared in journals including the Journal of the European Mathematical Society, Advances in Mathematics, Proceedings of the London Mathematical Society, and The Journal of Symbolic Logic.
邀请人：何家亮
