Anush Tserunyan

Անուշ Ծերունյան

Preprints

• Tree-like graphings, wallings, and median graphings of equivalence relations [arXiv] (2023+)
  ▻with Ruiyuan (Ronnie) Chen, Antoine Poulin, and Ran Tao
• Nonamenable subforests of multi-ended quasi-pmp graphs [arXiv] (2022+)
  ▻with Ruiyuan (Ronnie) Chen and Grigory Terlov
• Markers and the ratio ergodic theorem via tiling [arXiv] (2022+)
  ▻with Benjamin Miller
• A backward ergodic theorem along trees and its consequences for free group actions [arXiv] (2021+)
  ▻with Jenna Zomback
• Edge sliding and ergodic hyperfinite decomposition [arXiv] (2017+)
  ▻with Benjamin Miller

Publications

• Pairs of disjoint matchings and related classes of graphs [arXiv, DOI]
  ▻with H. Guo, K. Kaempen, Z. Mo, S. Qunell, J. Rogge, C. Song, J. Zomback
  Involve, a Journal of Mathematics 16-2 (2023), 249–264

• Mixing and double recurrence in probability groups [arXiv, DOI]
  Fundamenta Mathematicae 260 (2023), 77–98
• Pointwise ergodic theorem for locally countable quasi-pmp graphs [arXiv, DOI]
  Journal of Modern Dynamics, 18 (2022), 609–655
• Characterization of saturated graphs related to pairs of disjoint matchings [arXiv, DOI]
  ▻with Zhengda Mo, Samuel Qunell, and Jenna Zomback
  Illinois J. Math. 66(1): 59–77 (2022)
• Independent sets in algebraic hypergraphs [arXiv, DOI]
  ▻with Anton Bernshteyn and Michelle Delcourt
  Journal of the European Math. Soc. (published online, 2021)
• A descriptive construction of trees and Stallings' theorem [arXiv, DOI]
  Trends in set theory, Contemporary Mathematics, vol. 752 (2020), Amer. Math. Soc., Providence, RI, pp. 191–207
• A short nonalgorithmic proof of the containers theorem for hypergraphs [arXiv, DOI]
  ▻with Anton Bernshteyn, Michelle Delcourt, and Henry Towsner
  Proceedings of the American Math. Soc., vol. 147 (2019), pp. 1739–1749

• A Ramsey theorem on semigroups and a general van der Corput lemma [arXiv, DOI]
  Journal of Symbolic Logic, vol. 81 (2016), no. 2, pp. 718–741
• Finite generators for countable group actions in the Borel and Baire category settings [arXiv, DOI]
  Advances in Mathematics, vol. 269 (2015), pp. 585–646
• Characterization of a class of graphs related to pairs of disjoint matchings [arXiv, DOI]
  Discrete Mathematics, vol. 309 (2009), no. 4, pp. 693–713
• On edge-disjoint pairs of matchings [arXiv, DOI]
  ▻with Vahan Mkrtchyan and Vahé Musoyan
  Discrete Mathematics, vol. 308 (2008), no. 23, pp. 5823–5828

Supervised undergraduate research

• Alexandra (Sasha) Bell and Owen Rodgers, A modern exposition of Kakutani’s criterion for equivalence of product measures, McGill Undergraduate Research Project, Summer 2023 [pdf]
• Thomas Buffard, Gabriel Levrel, and Sam Mayo, Borel Determinacy: a streamlined proof, McGill Undergraduate Research Project, Fall 2021 [pdf]

Ph.D. Thesis

Finite generators for countable group actions; Finite index pairs of equivalence relations; Complexity measures for recursive programs [pdf, ProQuest]

UCLA (May, 2013)

Other writing

• A descriptive set theorist's proof of the pointwise ergodic theorem [arXiv]
  Oberwolfach, Germany (2017)
• Realizations of graphs in a Hilbert space [pdf]
  (with Terence Tao) Banff International Research Station, Canada (July, 2015)
• The Effros space of a σ-Polish space is standard Borel [pdf]
  UIUC (January, 2014)
• Countable compact Hausdorff spaces are Polish [pdf]
  UCLA (March, 2013)
• Segal's effective witness to measure-hyperfiniteness [pdf]
  Caltech (Fall, 2012)
• Hjorth's proof of the embeddability of hyperfinite equivalence relations into E₀ [pdf]
  UCLA (Fall, 2010)

Contributions in others' works

• Y. Moschovakis, Abstract Recursion and Intrinsic Complexity, to appear in the ASL Lecture Notes in Logic (2018) [pdf]
  Section 3B consists of the results of Part 3 of my Ph.D. thesis on complexity measures for recursive programs.
  UCLA (Fall, 2009)
• A. Kechris, The spaces of measure preserving equivalence relations and graphs, preprint (2017) [pdf]
  Sections 3, 6, 19 contain some of my results regarding the weak and strong topologies, the discontinuity of the map from actions to equivalence relations, and subtreeings of treeings of an equivalence relation.
  Caltech (Spring, 2013)
• M. Lupini, Polish groupoids and functorial complexity, Trans. of the Amer. Math. Soc., 369 (2017), no. 9, 6683–6723 [arXiv]
  Appendix consists of my proof of the Effros space of a σ-Polish space being standard Borel. [pdf]
  UIUC (January, 2014)