Ruiyuan (Ronnie) Chen

Teaching

• Fall 2024: Math 403 (Intro to discrete math) [Canvas]
• Fall 2024: Math 481 (Mathematical logic) [Canvas]

Seminars

Papers

• Structurable equivalence relations and $\mathcal L_{\omega_1\omega}$ interpretations
  (with R. Banerjee)
  submitted (2024) [pdf] [arXiv]
• Clones of Borel Boolean functions
  (with I. Ziba)
  submitted (2024) [pdf] [arXiv]
• Structural, point-free, non-Hausdorff topological realization of Borel groupoid actions
  Forum Math. Sigma 12 (2024) [pdf] [arXiv] [journal]
• A Gelfand duality for continuous lattices
  Theory Appl. Categ. 41 (2024) [pdf] [arXiv] [journal]
• Étale structures and the Joyal–Tierney representation theorem in countable model theory
  submitted (2023) [pdf] [arXiv]
• Nonamenable subforests of multi-ended quasi-pmp graphs
  (with G. Terlov and A. Tserunyan)
  submitted (2023) [pdf] [arXiv]
• Tree-like graphings, wallings, and median graphings of equivalence relations
  (with A. Poulin, R. Tao, and A. Tserunyan)
  submitted (2023) [pdf] [arXiv]
• A universal characterization of standard Borel spaces
  J. Symb. Logic 88 (2023) [pdf] [arXiv] [journal]
• On sifted colimits in the presence of pullbacks
  Theory Appl. Categ. 37 (2021) [pdf] [arXiv] [journal]
• On the Pettis–Johnstone theorem for localic groups
  submitted (2021) [pdf] [arXiv]
• Decompositions and measures on countable Borel equivalence relations
  Ergodic Theory Dynam. Systems 41 (2021) [pdf] [arXiv] [journal]
• Borel and analytic sets in locales
  preprint (2020) [pdf] [arXiv]
• Bounds on continuous Scott rank
  (with W. Chan)
  Proc. Amer. Math. Soc. 148 (2020) [pdf] [arXiv] [journal]
• Representing Polish groupoids via metric structures
  preprint (2019) [pdf] [arXiv]
• Borel functors, interpretations, and strong conceptual completeness for $\mathcal L_{\omega_1\omega}$
  Trans. Amer. Math. Soc. 372 (2019) [pdf] [arXiv] [journal]
• Amalgamable diagram shapes
  J. Symb. Logic 84 (2019) [pdf] [arXiv] [journal]
• Notes on quasi-Polish spaces
  preprint (2018) [pdf] [arXiv]
• Borel structurability by locally finite simplicial complexes
  Proc. Amer. Math. Soc. 146 (2018) [pdf] [arXiv] [journal]
• Structurable equivalence relations
  (with A. S. Kechris)
  Fund. Math. 242 (2018) [pdf] [arXiv] [journal]
• Forbidden submatrices: some new bounds and constructions
  (with R. P. Anstee)
  Electron. J. Combin. 20 (2013) [pdf] [journal]

Notes

• On the Lusin–Suslin and Lusin unicity theorems [pdf]
• On Gaboriau's homological proof that treeings achieve cost [pdf]
• Products of Scott topologies and spatiality [pdf]
• A geometric proof that $S_0 \times S_0$ is not spatial [pdf]
• On Lusin–Novikov uniformization [pdf]
• On uniform ergodic decomposition [pdf]
• A topological proof of the boundedness theorem for $\mathbf{\Sigma}^1_1$ well-founded relations [pdf]
• A simple proof of the Lusin–Suslin theorem [pdf]