Aareyan Manzoor

I am a grad student at Waterloo. My current interests are in the intersection of operator algebras and quantum information. I am a former bangladeshi but current ontorian, and I am a member of the LGBTQ+ community

I will post papers, talks etc here.

Papers

  1. Locally Universal Tracial von Neumann Algebras Have Undecidable Universal Theory, August 2025, arXiv:2508.21709, with Jananan Arulseelan.
    Abstract Building on Lin’s breakthrough MIP$^{co}$=coRE and an encoding of non-local games as universal sentences in the language of tracial von Neumann algebras, we show that locally universal tracial von Neumann algebras have undecidable universal theories. This implies that no such algebra admits a computable presentation. Our results also provide, for the first time, explicit examples of separable II$_1$ factors without computable presentations, and in fact yield a broad family of them, including McDuff factors, factors without property $\Gamma$, and property (T) factors. We also obtain analogous results for locally universal semifinite von Neumann algebras and tracial $C^*$-algebras. The latter provides strong evidence for a negative solution to the Kirchberg embedding problem. We discuss how these are obstructions to approximation properties in the class of tracial/semifinite von Neumann algebras.
  2. Invariant Random Subgroups, Soficity, and Lück’s determinant conjecture, August 2025, arXiv:2508.15154
    Abstract 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. For every free group, we prove the existence of an IRS satisfying the determinant conjecture that is not co-hyperlinear, and hence not co-sofic. This provides evidence that satisfying the determinant conjecture might be a weaker property than soficity for groups, and consequently the conjecture possibly holds for all groups. We use techniques from non-local games and MIP* = RE, showing more generally when the latter can be used to narrow down when a von Neumann algebra (or IRS) contains a non-Connes embeddable object.
  3. There Is An Equivalence Relation Whose von Neumann Algebra Is Not Connes Embeddable, February 2025, arXiv:2502.06697
    Abstract 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 a negative solution to the Aldous-Lyons conjecture: there is a non co-sofic IRS on any non-abelian free group. We define a notion of hyperlinearity for an IRS and show that there is a non co-hyperlinear IRS on any non-abelian free group. As a corollary, we prove that there is a relation whose von Neumann algebra is not Connes embeddable. We do this by significantly simplifying the reduction of Aldous-Lyons to non-local games, removing the need for subgroup tests entirely.

Quantum PCP (Master’s Thesis, University of Waterloo — July 2024)

Abstract / Description I survey the Quantum PCP conjecture, discussing the NLTS theorem, quantum error-correcting codes, complexity-theoretic preliminaries, and more. At Waterloo, the master’s thesis is really meant to be expository and generally doesn’t contain new results — but I do show that a bound for CSS local testability in the literature is off by a constant.

Seminar/Conference Talks

Here are talks I have given at seminars/conferences.

Seminars

I am not running any seminars currently. These are seminars that I have run before:
  • Quantum PCPs seminar, Spring+Winter 2024 at Waterloo.

    • Teaching

    Here are some things I have done beyond just TAing:

    Other Talks

    Here are my talk slides/recorded talks:
  • Model theory of II_1 factors, for an introductory course on tracial von Nuemann algebras.
  • The complexity class QMA, for an introductory course in quantum information.
  • On the (co)homology of spectra for an seminar on stable homotopy theory
  • Brown representability same seminar