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math.OA2026★ 1 cited
The Universal Theory of Locally Universal Tracial von Neumann Algebras is not Computable
Jananan Arulseelan, Aareyan Manzoor
Building on Lin's breakthrough MIP = coRE and an encoding of non-local games as universal sentences in the language of tracial von Neumann algebras, we show that locally uni…
math.OA2026
There Is An Equivalence Relation Whose von Neumann Algebra Is Not Connes Embeddable
Aareyan Manzoor
The landmark quantum complexity result MIP=RE was used to prove the existence of a non Connes embeddable tracial von Neumann algebra. Recently, similar ideas were used to give…
math.OA2025
Invariant Random Subgroups, Soficity, and Lück's determinant conjecture
Aareyan Manzoor
We extend Lück's determinant conjecture from groups to invariant random subgroups (IRS) of free groups, a framework generalizing groups where a non-sofic object is known to exist.…