Ronnie Chen

Teaching

Past courses at UMich

Winter 2025: Math 417 (Linear algebra)
Winter 2025: Math 582 (Set theory) [notes]
Fall 2024: Math 403 (Intro to discrete math)
Fall 2024: Math 481 (Mathematical logic) [notes 1 2 A]
Winter 2024: Math 419 (Linear algebra)
Winter 2024: Math 582 (Set theory)
Fall 2023: Math 403 (Intro to discrete math)
Fall 2023: Math 682 (Descriptive set theory)
Winter 2023: Math 419 (Linear algebra)
Winter 2023: Math 582 (Set theory)
Fall 2022: Math 417 (Matrix algebra)
Fall 2022: Math 481 (Mathematical logic)

Past courses at UIUC

Spring 2021: Math 414 (Mathematical logic)
Spring 2021: Math 416 (Abstract linear algebra)
Fall 2020: Math 347 Honors (Fundamental mathematics)
Spring 2020: Math 414 (Mathematical logic)
Fall 2019: Math 416 (Abstract linear algebra)
Fall 2019: Math 595 (Advanced topics: categorical logic) [unfinished notes]
Spring 2019: Math 347 Honors (Fundamental mathematics)
Fall 2018: Math 403 (Euclidean geometry)

Papers

Componentwise Polish groupoids and equivalence relations
preprint (2025) [pdf] [arXiv]
Étale structures and the Joyal–Tierney representation theorem in countable model theory
to appear in Bull. Symb. Logic (2025) [pdf] [arXiv] [journal]
Optimal syntactic definitions of back-and-forth types
(with D. Gonzalez and M. Harrison-Trainor)
submitted (2025) [pdf] [arXiv]
Tree-like graphings, wallings, and median graphings of equivalence relations
(with A. Poulin, R. Tao, and A. Tserunyan)
Forum Math. Sigma 13 (2025) [pdf] [arXiv] [journal]
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]
Nonamenable subforests of multi-ended quasi-pmp graphs
(with G. Terlov 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 large section uniformization theorem [pdf]
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]