Ronnie Chen

Teaching

Past courses at UIUC

Cardinal algebras, Borel fields of structures, and $\ell^2$-Betti numbers
in preparation (2022+)
Cardinal algebras, $[0, \infty]$-enriched frames, and valuation locales
in preparation (2022+)
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]
Borel and analytic sets in locales
preprint (2020) [pdf] [arXiv]
Decompositions and measures on countable Borel equivalence relations
Ergodic Theory Dynam. Systems 41 (2021) [pdf] [arXiv] [journal]
Bounds on continuous Scott rank
(with W. Chan)
Proc. Amer. Math. Soc. 148 (2020) [pdf] [arXiv] [journal]
A universal characterization of standard Borel spaces
submitted (2019) [pdf] [arXiv]
Representing Polish groupoids via metric structures
submitted (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]

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]