UCI Mathematics Department
All of my teaching materials are on canvas. Here is my cv and a research statement.
Large fields and the étale open topology
This talk gives an introduction for logicians and
this talk gives an introduction for a more general audience.
Dave Marker's lecture notes gives a discussion of the result on large stable fields. It is probably more acessible to model theorists than our original paper..
The étale-open topology and the stable field conjecture,
with Will Johnson, Minh Chieu Tran, and Vincent Ye. Accepted in JEMS.
Galois groups of large fields with simple theory, with Anand Pillay.
Éz fields, with Vincent Ye.
Topological proofs of results on large fields, accepted in Comptes Rendus (pending revisions).
The étale open topology over the fraction field of a Henselian local domain I, with Will Johnson and Vincent Ye.
General model theory
Interpolative Fusions I, with Alex Kruckman and Minh Chieu Tran. Journal of Mathematical Logic.
Notes on trace equivalence..
Logic over the real line
A presentation of the proof of the NIP case of the main conjecture on expansions of (R,<,+). (The proof is given in a more general setting here.)
Interpreting the Monadic Second Order Theory of One Successor in Expansions of the Real Line, with Philipp Hieronymi, Isreal Journal of Mathematics.
How to avoid a compact set, with Antongiulio Fornasiero and Philipp Hieronymi, Advances in Mathematics.
Wild theories with o-minimal open core, with Philipp Hieronymi and Travis Nell. Annals of Pure and Applied logic.
A tetrachotomy for expansions of the real ordered additive group, with Philipp Hieronymi. Selecta Mathematica.
Expansions of the real field by discrete subgroups of Gln(C) with Philipp Hieronymi and Samantha Xu. Proceedings of the AMS.
Fractals and the monadic second order theory of one sucessor with Philipp Hieronymi.
Continuous Regular Functions, with Alexi Block Gorman, Elliot Kaplan, Philipp Hieronymi, Ruoyu Meng, Zihi Wang, Ziqin Xiong, and Hongru Yang. Logical Methods in Computer Science.
Coarse dimension and definable sets in expansions of the ordered real vector space. Illinois Journal of Mathematics.
The independence property
Externally definable quotients and NIP expansions of the real ordered additive group. Transactions of the AMS.
Dp-minimal valued fields, with Franziska Jahnke and Pierre Simon. Journal of Symbolic Logic.
Dp and other minimalities with Pierre Simon. Journal of Symbolic Logic.
Tame topology over dp-minimal structures, with Pierre Simon, Notre Dame Journal of Formal Logic.
A family of dp-minimal expansions of the additive group of integers, with Minh Chieu Tran. NDJFL.
Dp-minimal expansions of (Z,+) via dense pairs via Mordell-Lang
Nippy proofs of p-adic results of Delon and Yao
The Marker-Steinhorn Theorem via definable linear orders, Notre Dame Journal of Formal Logic.
Hausdorff dimension of definable metric spaces in o-minimal expansions of the real field., with Jana Maříková. Fundamenta Mathematicae.
Directed sets and topological spaces definable in o-minimal structures. with Pablo Andujar Guerrero and Margaret Thomas. Journal of the London Mathematical Society.