@article{AaronsonLinWeiss1979,
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@article{ArzhantsevaEtAl2005,
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@article{Atabekyan2008,
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@book{BekkaHarpeValette2008,
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  year      = {2008},
  doi       = {10.1017/CBO9780511542749}
}

@article{BergelsonRosenblatt1988,
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  title   = {Mixing actions of groups},
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  year    = {1988},
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@article{CluckersEtAl2011,
  author  = {Cluckers, Raf and Cornulier, Yves and Louvet, Nicolas and Tessera, Romain and Valette, Alain},
  title   = {The {H}owe--{M}oore property for real and \(p\)-adic groups},
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  number  = {2},
  year    = {2011},
  pages   = {201--224},
  doi     = {10.7146/math.scand.a-15185}
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@article{ConnesWeiss1980,
  author  = {Connes, Alain and Weiss, Benjamin},
  title   = {Property {T} and asymptotically invariant sequences},
  journal = {Israel J. Math.},
  volume  = {37},
  year    = {1980},
  pages   = {209--210},
  doi     = {10.1007/BF02760962}
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@article{Dye1965,
  author  = {Dye, Henry A.},
  title   = {On the ergodic mixing theorem},
  journal = {Trans. Amer. Math. Soc.},
  volume  = {118},
  year    = {1965},
  pages   = {123--130},
  doi     = {10.1090/S0002-9947-1965-0174705-8}
}

@incollection{FurstenbergWeiss1978,
  author    = {Furstenberg, Harry and Weiss, Benjamin},
  title     = {The finite multipliers of infinite ergodic transformations},
  booktitle = {The Structure of Attractors in Dynamical Systems},
  series    = {Lecture Notes in Mathematics},
  volume    = {668},
  publisher = {Springer},
  address   = {Berlin},
  year      = {1978},
  pages     = {127--132},
  doi       = {10.1007/BFb0101785}
}

@article{GelanderZuk2002,
  author  = {Gelander, Tsachik and {\.{Z}}uk, Andrzej},
  title   = {Dependence of {K}azhdan constants on generating subsets},
  journal = {Israel J. Math.},
  volume  = {129},
  year    = {2002},
  pages   = {93--98},
  doi     = {10.1007/BF02773155}
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@book{Glasner2003,
  author    = {Glasner, Eli},
  title     = {Ergodic Theory via Joinings},
  series    = {Mathematical Surveys and Monographs},
  volume    = {101},
  publisher = {American Mathematical Society},
  address   = {Providence, RI},
  year      = {2003},
  doi       = {10.1090/surv/101}
}

@incollection{Gromov1987,
  author    = {Gromov, Mikhail},
  title     = {Hyperbolic groups},
  booktitle = {Essays in Group Theory},
  editor    = {Gersten, S. M.},
  series    = {Mathematical Sciences Research Institute Publications},
  volume    = {8},
  publisher = {Springer},
  address   = {New York},
  year      = {1987},
  pages     = {75--263},
  doi       = {10.1007/978-1-4613-9586-7_3}
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@article{Hadad2007,
  author  = {Hadad, Uzy},
  title   = {Uniform {K}azhdan constant for some families of linear groups},
  journal = {J. Algebra},
  volume  = {318},
  number  = {2},
  year    = {2007},
  pages   = {607--618},
  doi     = {10.1016/j.jalgebra.2007.08.012}
}

@article{HawkinsSilva1998,
  author  = {Hawkins, Jane and Silva, C. E.},
  title   = {Characterizing mildly mixing actions by orbit equivalence of products},
  journal = {New York J. Math.},
  volume  = {3A},
  year    = {1998},
  pages   = {99--115}
}

@article{HoweMoore1979,
  author  = {Howe, Roger E. and Moore, Calvin C.},
  title   = {Asymptotic properties of unitary representations},
  journal = {J. Funct. Anal.},
  volume  = {32},
  number  = {1},
  year    = {1979},
  pages   = {72--96},
  doi     = {10.1016/0022-1236(79)90078-8}
}

@article{Hull2016,
  author  = {Hull, Michael},
  title   = {Small cancellation in acylindrically hyperbolic groups},
  journal = {Groups Geom. Dyn.},
  volume  = {10},
  number  = {4},
  year    = {2016},
  pages   = {1077--1119},
  doi     = {10.4171/GGD/377}
}

@article{IvanovOlshanskii1996,
  author  = {Ivanov, S. V. and Ol'shanskii, A. Yu.},
  title   = {Hyperbolic groups and their quotients of bounded exponents},
  journal = {Trans. Amer. Math. Soc.},
  volume  = {348},
  number  = {6},
  year    = {1996},
  pages   = {2091--2138},
  doi     = {10.1090/S0002-9947-96-01510-3}
}

@article{JonesSchmidt1987,
  author  = {Jones, Vaughan F. R. and Schmidt, Klaus},
  title   = {Asymptotically invariant sequences and approximate finiteness},
  journal = {Amer. J. Math.},
  volume  = {109},
  number  = {1},
  year    = {1987},
  pages   = {91--114},
  doi     = {10.2307/2374553}
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@article{Kazhdan1967,
  author  = {Kazhdan, David A.},
  title   = {Connection of the dual space of a group with the structure of its closed subgroups},
  journal = {Funct. Anal. Appl.},
  volume  = {1},
  year    = {1967},
  pages   = {63--65},
  doi     = {10.1007/BF01075866}
}

@book{Kechris2010,
  author    = {Kechris, Alexander S.},
  title     = {Global Aspects of Ergodic Group Actions},
  series    = {Mathematical Surveys and Monographs},
  volume    = {160},
  publisher = {American Mathematical Society},
  address   = {Providence, RI},
  year      = {2010},
  doi       = {10.1090/surv/160}
}

@book{Lubotzky1994,
  author    = {Lubotzky, Alexander},
  title     = {Discrete Groups, Expanding Graphs and Invariant Measures},
  series    = {Progress in Mathematics},
  volume    = {125},
  publisher = {Birkh{\"a}user},
  address   = {Basel},
  year      = {1994}
}

@article{Mayer1997,
  author  = {Mayer, Matthias},
  title   = {Strongly mixing groups},
  journal = {Semigroup Forum},
  volume  = {54},
  number  = {3},
  year    = {1997},
  pages   = {303--316},
  doi     = {10.1007/BF02676613}
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@article{Olshanskii1979,
  author  = {Ol'shanskii, A. Yu.},
  title   = {Infinite groups with cyclic subgroups},
  journal = {Soviet Math. Dokl.},
  volume  = {20},
  number  = {2},
  year    = {1979},
  pages   = {343--346}
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@article{Olshanskii1992,
  author  = {Ol'shanskii, A. Yu.},
  title   = {Periodic factor groups of hyperbolic groups},
  journal = {Math. USSR-Sb.},
  volume  = {72},
  number  = {2},
  year    = {1992},
  pages   = {519--541},
  doi     = {10.1070/SM1992v072n02ABEH002149}
}

@article{Olshanskii1993,
  author  = {Ol'shanskii, A. Yu.},
  title   = {On residualing homomorphisms and {$G$}-subgroups of hyperbolic groups},
  journal = {Internat. J. Algebra Comput.},
  volume  = {3},
  number  = {4},
  year    = {1993},
  pages   = {365--409},
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@book{Olshanskii1991Book,
  author    = {Ol'shanskii, A. Yu.},
  title     = {Geometry of Defining Relations in Groups},
  series    = {Mathematics and Its Applications (Soviet Series)},
  volume    = {70},
  publisher = {Kluwer Academic Publishers},
  address   = {Dordrecht},
  year      = {1991},
  doi       = {10.1007/978-94-011-3618-1}
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@article{Osin2002,
  author  = {Osin, Denis V.},
  title   = {Kazhdan constants of hyperbolic groups},
  journal = {Funct. Anal. Appl.},
  volume  = {36},
  number  = {4},
  year    = {2002},
  pages   = {290--297},
  doi     = {10.1023/A:1021761810280}
}

@article{Osin2007,
  author  = {Osin, Denis V.},
  title   = {Uniform non-amenability of free {B}urnside groups},
  journal = {Arch. Math. (Basel)},
  volume  = {88},
  number  = {5},
  year    = {2007},
  pages   = {403--412},
  doi     = {10.1007/s00013-006-2002-5}
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@misc{OsinSonkin2006,
  author        = {Osin, Denis and Sonkin, Dmitriy},
  title         = {Uniform {K}azhdan groups},
  year          = {2006},
  eprint        = {math/0606012},
  archivePrefix = {arXiv},
  note          = {arXiv:math/0606012v1, 1 June 2006; no journal or
                   proceedings publication identified as of
                   29 August 2026}
}

@article{Ozawa2004,
  author  = {Ozawa, Narutaka},
  title   = {There is no separable universal {$\mathrm{II}_1$}-factor},
  journal = {Proc. Amer. Math. Soc.},
  volume  = {132},
  number  = {2},
  year    = {2004},
  pages   = {487--490},
  doi     = {10.1090/S0002-9939-03-07127-2}
}

@article{Pham2022,
  author  = {Pham, L. L.},
  title   = {Uniform {K}azhdan constants and paradoxes of the affine plane},
  journal = {Transform. Groups},
  volume  = {27},
  number  = {1},
  year    = {2022},
  pages   = {239--269},
  doi     = {10.1007/s00031-020-09600-5}
}

@article{Rostami2008,
  author  = {Rostami, Hamid Reza},
  title   = {About groups with property ({U})},
  journal = {Armenian J. Math.},
  volume  = {1},
  number  = {3},
  year    = {2008},
  pages   = {14--22}
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@article{Schmidt1981,
  author  = {Schmidt, Klaus},
  title   = {Amenability, {K}azhdan's property {T}, strong ergodicity and invariant means for ergodic group-actions},
  journal = {Ergodic Theory Dynam. Systems},
  volume  = {1},
  number  = {2},
  year    = {1981},
  pages   = {223--236},
  doi     = {10.1017/S014338570000924X}
}

@article{Schmidt1984,
  author  = {Schmidt, Klaus},
  title   = {Asymptotic properties of unitary representations and mixing},
  journal = {Proc. London Math. Soc. (3)},
  volume  = {48},
  number  = {3},
  year    = {1984},
  pages   = {445--460},
  doi     = {10.1112/plms/s3-48.3.445}
}

@article{SchmidtWalters1982,
  author  = {Schmidt, Klaus and Walters, Peter},
  title   = {Mildly mixing actions of locally compact groups},
  journal = {Proc. London Math. Soc. (3)},
  volume  = {45},
  number  = {3},
  year    = {1982},
  pages   = {506--518},
  doi     = {10.1112/plms/s3-45.3.506}
}

@article{Schur1911,
  author  = {Schur, Issai},
  title   = {{\"U}ber Gruppen periodischer linearer Substitutionen},
  journal = {Sitzungsber. K\"onigl. Preuss. Akad. Wiss. Berlin},
  year    = {1911},
  pages   = {619--627}
}

@article{Semenov1993,
  author  = {Semenov, Yu. S.},
  title   = {Some quotient groups of hyperbolic groups},
  journal = {Moscow Univ. Math. Bull.},
  volume  = {48},
  number  = {3},
  year    = {1993},
  pages   = {39--40},
  note    = {English translation; Russian original: Vestnik Moskov.
             Univ. Ser. 1 Mat. Mekh. (1993), no. 3, 88--90}
}

@phdthesis{SemenovThesis1994,
  author = {Semenov, Yu. S.},
  title  = {Some Constructions of Quotient Groups and Rings for
            Hyperbolic Groups},
  school = {Moscow State University},
  year   = {1994},
  note   = {Russian. Osin--Sonkin and Kulikova give 1994; the
            author's 2017 manuscript gives 1995}
}

@misc{Semenov2017Full,
  author = {Semenov, Yu. S.},
  title  = {On Quotients of Torsion-Free Hyperbolic Groups},
  year   = {2017},
  note   = {31-page author manuscript uploaded to ResearchGate on
            25 April 2017; no journal, proceedings, DOI, or arXiv
            publication identified as of 29 August 2026},
  url    = {https://www.researchgate.net/publication/316464601_ON_QUOTIENTS_OF_TORSION-FREE_HYPERBOLIC_GROUPS}
}

@article{Kulikova2023,
  author  = {Kulikova, O. V.},
  title   = {On Some Quotients of Hyperbolic Groups},
  journal = {Math. Notes},
  volume  = {114},
  number  = {1},
  year    = {2023},
  pages   = {99--107},
  doi     = {10.1134/S0001434623070106}
}

@incollection{Walters1983,
  author  = {Walters, Peter},
  title   = {A mixing property for non-singular actions},
  booktitle = {Bifurcation, th{\'e}orie ergodique et applications},
  series  = {Ast{\'e}risque},
  number  = {98--99},
  publisher = {Soci{\'e}t{\'e} math{\'e}matique de France},
  year    = {1982},
  pages   = {163--183}
}

@misc{Yao2026,
  author        = {Yao, Jvbin},
  title         = {Finite direct-product quotients and uniform {K}azhdan constants},
  year          = {2026},
  eprint        = {2608.03561},
  archivePrefix = {arXiv},
  primaryClass  = {math.GR},
  howpublished  = {\url{https://arxiv.org/abs/2608.03561v1}},
  note          = {Preprint, 4 August 2026, arXiv:2608.03561v1}
}

@incollection{Connes1982,
  author    = {Connes, Alain},
  title     = {Classification des facteurs},
  booktitle = {Operator Algebras and Applications, Part 2
               (Kingston, Ont., 1980)},
  series    = {Proc. Sympos. Pure Math.},
  volume    = {38},
  publisher = {American Mathematical Society},
  address   = {Providence, RI},
  year      = {1982},
  pages     = {43--109},
  doi       = {10.1090/pspum/038.2/679497}
}

@misc{OpenAI2026TenAdvances,
  author = {{OpenAI}},
  title  = {{Ten Advances in Mathematics and Theoretical Computer Science}},
  year   = {2026},
  month  = aug,
  url    = {https://cdn.openai.com/pdf/ten-proofs-oai.pdf},
  note   = {Updated 6 August 2026; Chapter 4, A Counterexample to
            Connes's Rigidity Conjecture, pp. 96--113}
}

@misc{Zhou2026ICC,
  author        = {Zhou, Shuoxing},
  title         = {{ICC} Property~{(T)} Groups without
                   {$W^*$}-Superrigidity},
  year          = {2026},
  eprint        = {2608.02327},
  archivePrefix = {arXiv},
  primaryClass  = {math.OA},
  doi           = {10.48550/arXiv.2608.02327},
  url           = {https://arxiv.org/abs/2608.02327},
  note          = {Version 1, submitted 3 August 2026}
}

@misc{xu2026agents,
  author       = {Xu, Chao},
  title        = {{AI} Agents for the Working Mathematician},
  year         = {2026},
  month        = jul,
  howpublished = {\url{https://chaoxu.prof/posts/2026-07-18-ai-agents-for-the-working-mathematician.html}},
  note         = {Posted 18 July 2026; revised 19 September 2026.
                  Accessed 7 October 2026}
}

@misc{LubotzkyYao2026,
  author        = {Lubotzky, Alexander and Yao, Jvbin},
  title         = {Non Uniform {Kazhdan} Constant for Linear Groups},
  year          = {2026},
  month         = aug,
  eprint        = {2608.03561v2},
  archivePrefix = {arXiv},
  primaryClass  = {math.GR},
  howpublished  = {\url{https://arxiv.org/abs/2608.03561v2}},
  note          = {Version 2, 31 August 2026}
}