Papers

Last updated 02/08/2026

Research Articles:

  1. S Bardyla, L Elliott. Polish topologies on endomorphism monoids of linear orders, 2026[Submitted to Journal of the Institute of Mathematics of Jussieu]

  2. L Elliott, A Levine. Commutative decomposition of infinite symmetric groups and transformation monoids, 2026[Submitted to Bulletin of the London Mathematical Society]

  3. L Elliott, A Evetts and A Levine. Counting Automorphic Orbits in Finitely Generated Groups, 2026[Submitted to Canadian journal of mathematics]

  4. L Elliott, The Zariski Topology on Homeomorphism groups, 2026 Published in Topology and its Applications

  5. S Bardyla, L Elliott, J Mitchell and Y Peresse. A note on intrinsic topologies of groups, 2025[Submitted to Journal of Algebra]

  6. A Levine and L Elliott. The Diophantine problem in Thompson’s group F, 2025 Published in Mathematics of Computation

  7. R Al Kohli, C Bleak and L Elliott. On epiC groups over language class C, 2025[Submitted to Journal of Algebra]

  8. L Elliott, A Levine and J Mitchell. Computing congruences of finite inverse semigroups, 2024

  9. S Bardyla, L Elliott, J Mitchell and Y Peresse. Classifying the Polish semigroup topologies on the symmetric inverse monoid, 2024 Published in Proceedings of the Edinburgh Mathematical Society

  10. L Elliott, A Levine and J Mitchell. E-disjunctive inverse semigroups, 2024 Published in Journal of Algebra

  11. B de Witt and L Elliott. Finite Presentability of Brin-Higman-Thompson Monoids via Free J'onsson-Tarski Algebras, 2023[Submitted to Semigroup Forum]

  12. S Bardyla, L Elliott, J Mitchell and Y Peresse, Topological embeddings into transformation monoids, 2023 Published in Forum Mathematicum

  13. L Elliott, A Levine and J Mitchell. Counting monogenic monoids and inverse monoids, 2023 Published in Communications in Algebra

  14. L Elliott, J Jonusas, J Mitchell, Y Peresse and M Pinsker. Polish topologies on endomorphism monoids of relational structures, 2022 Published in Advances in Mathematics

  15. J Belk, L Elliott and F Matucci. A short proof of Rubin’s theorem, 2022 Published in Israel Journal of Mathematics

  16. L Elliott. Unindexed subshifts of finite type and their connection to automorphisms of Thompson’s groups, 2021

  17. L Elliott, J Jonusas, Z Mesyan, J Mitchell, M Morayne and Y Peresse. Automatic continuity, unique Polish topologies, and Zariski topologies on monoids and clones, 2021 Published in Transactions of the American Mathematical Society

  18. L Elliott. A description of Aut(dVn) and Out(dVn) using transducers, 2020 Publised in Groups, Geometry, and Dynamics

  19. C Bleak, L Elliott and J Hyde, Sufficient conditions for a group of homeomorphisms of the cantor set to be two-generated, 2020 Published in Journal of the Institute of Mathematics of Jussieu

Master’s Thesis

Infinite Symmetric Groups

PhD Thesis

On constructing topology from algebra

Other random info luna wanted to track:

Currently working on more projects with the following authors [L Elliott], [L Elliott + A Levine], [L Elliott + G Crowe], [L Elliott + S Bardyla]x2, [L Elliott + S Bardyla + Y Peresse], [L Elliott + R Cirpons + A Levine + J Mitchell], [L Elliott + N Kolodny].

Average paper length: \(\frac{37+17+52+39+10+21+9+19+23+38+23+22+21+10+12+13+43+12+21}{19} \approx 23.26\) pages.

11/19 of lunas papers are currently published in journals.

Articles that have cited Luna’s papers as of 02/06/2026 (excluding papers already mentioned above):

  1. K Arana, J Pérez and C Uzcátegui, Pettis property for Polish inverse semigroups

  2. T Banakh and S Bardyla, Categorically closed countable semigroups

  3. S Bardyla, Countably compact inverse semigroups and Nyikos’ problem

  4. E Bashwinger and P DeBonis, On Similarity Structure Groups and their W* and C*-Algebras

  5. J Belk, J Hyde and F Matucci, Finite germ extensions

  6. J Belk, MCB Zaremsky, Twisted Brin–Thompson groups

  7. J Belk, C Bleak, F Matucci and MCB Zaremsky, Hyperbolic groups satisfy the Boone-Higman conjecture

  8. J Belk, C Bleak, M Quick and R Skipper, Type systems and maximal subgroups of Thompson’s group 𝑉

  9. J Birget, Some properties of Higman-Thompson monoids and digital circuits

  10. C Bleak, C Donoven, S Harper, J Hyde, Generating simple vigorous groups

  11. A Brothier and R Seelig, Finitely presented simple groups with no piecewise projective actions

  12. A Brothier, R Seelig, Forest-skein groups IV: dynamics

  13. C Bruce, X Li and T Takeishi, Boundary actions of outer automorphism groups of Thompson-like groups

  14. B Cameron, Abstract ping-pong systems in subgroups of Thompson’s groups

  15. A Carvalho and CF Nyberg-Brodda, On linguistic subsets of groups and monoids

  16. [F Flores, Mixed-identity-freeness and primitivity of group rings]

  17. G Goffer and B Greenfeld, A note on the Zariski topology on groups and semigroups

  18. J Gonzalez, Z Ghadernezhad, P Marimon, and M Pinsker, Minimal and intrinsic topologies on monoids of elementary embeddings

  19. R Gorazd, Higman–Thompson groups of unfolding trees of rooted graphs

  20. RD Gray and A Levine, Decidability of equations and first-order theory in Seifert 3-manifold groups

  21. RD Gray and A Levine, The Diophantine problem in the Baumslag-Gersten group

  22. RD Gray and A Levine, Undecidable diophantine problems in generalisations of one-relator groups

  23. J Gundelach, An embedding version of Rubin’s theorem

  24. S Harper, The spread of finite and infinite groups

  25. JE Hanson, T Koberda, J González and C Rosendal, Set theory, logic, and homeomorphism groups of manifolds

  26. M Hampenberg Christensen, Submonoids of Infinite Symmetric Inverse Monoids

  27. J Hyde, R Skipper and M Zaremsky, Action Graphs, Semiconjugacy, and Non-Embedding in Thompson’s Group V

  28. T Koberda and Y Lodha, Generic torsion-free groups and Rubin actions

  29. KL Kozlov, AG Leiderman, On proper compactifications of topological groups

  30. P Marimon and M Pinsker, A guide to topological reconstruction on endomorphism monoids and polymorphism clones

  31. P Marimon and M Pinsker, All mixed identities are singular in groups with no algebraicity

  32. M Megrelishvili, M Shlossberg, Non-archimedean topological monoids

  33. YA Neretin, Groups of isometries of ultrametric Urysohn spaces and their unitary representations

  34. OM Oladosu, Digraph generated by idempotents in certain finite semigroup of mappings

  35. M Palmer and X Wu, Embedding groups into acyclic groups

  36. J Perez and C Uzcategui, Topologies on the symmetric inverse semigroup

  37. D Perego and M Tarocchi, A class of rearrangement groups that are not invariably generated

  38. M Pinsker and C Schindler, The semigroup of increasing functions on the rational numbers has a unique Polish topology

  39. M Pinsker and C Schindler, On the Zariski topology on endomorphism monoids of omega-categorical structures

  40. M Pinsker, J Rydval, M Schöbi and C Spiess, Three Fundamental Questions in Modern Infinite-Domain Constraint Satisfaction

  41. KDA Romero, El semigrupo inverso simétrico, el teorema de Pettis y la continuidad automática

  42. E Rybak, Boundary dynamics, triple transitivity, and mixed identities in weakly hyperbolic groups

  43. R Sauer, E Schesler, A finitely presented group of non-uniform exponential growth

  44. C Schindler, Semigroup topologies on endomorphism monoids of omega-categorical structures

  45. O Tanner, Topological full groups

  46. M Tarocchi, Rearrangement Groups of Fractals: Structure and Conjugacy

  47. M Tarocchi, On Thompson groups for Ważewski dendrites

  48. MG Vio, C Kravaris and E Silva, The Poisson boundary of Thompson’s group is not the circle

  49. F Wu, X Wu, M Zhao and Z Zhou, Embedding groups into boundedly acyclic groups

  50. D Yang and W Yang, Homomorphism-homogeneous finite semilattices

Plan to read list:

ElementaryEmbeddings

TwistedConjugacy

InnerAutSemigroups

End(Q)

MarkovZariski

Out(V) act

Type Systems

Maths of Japanese

Mixed Identities

Alexandrov groups

Leavitt path algebras