5 papers
Humanity's Last Exam
Long Phan, Alice Gatti, Ziwen Han +1144
Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achi…
The Profinite Rigidity of Torsion-Free Lamplighter Groups
Nikolay Nikolov, Julian Wykowski
We prove that the torsion-free lamplighter group of any rank is profinitely rigid in the absolute sense: the finite quotients o…
The Profinite Rigidity of Free Metabelian Groups
Julian Wykowski
We prove that finitely generated free metabelian groups are profinitely rigid in the absolute sense: they are distinguished by their finite quotients among all finitely gene…
Profinite Rigidity over Noetherian Domains
Julian Wykowski
We initiate the study of profinite rigidity for modules over a Noetherian domain: to what extent are these objects determined by their finite images? We establish foundational stat…
Profinite Subgroup Accessibility and Recognition of Amalgamated Factors
Julian Wykowski
We investigate accessible subgroups of a profinite group , i.e. subgroups appearing as vertex groups in a graph of profinite groups decomposition of with finite edge gro…