My research area is model theory, a branch of mathematical logic. However, I would perhaps be better described as a “definable geometer”. My works explore interactions between model theory and other areas of mathematics like combinatorics, field arithmetic, and number theory.
Published and accepted papers
Model theory of Complex numbers with polynomial functions (with Benjamin Castle), arxiv:2308.01632, 2025, Selecta Mathematica
A Cauchy-Davenport theorem for locally compact groups (with Yifan Jing), arXiv:2106.02924, 2024, The Quarterly Journal of Mathematics, 2024
A nonabelian Brunn–Minkowski inequality (with Yifan Jing and Ruixiang Zhang), arXiv:2101.07782, 2021, Geometric and Functional Analysis 33 (4), 1048-1100. Ruixiang’s Talk.
The etale-open topology and the stable field conjecture (with Will Johnson, Erik Walsberg, and Jinhe Ye), arXiv:2009.02319, Journal of the European Mathematical Society 26 (10), 4033-4070. Erik’s Talk.
Stable formulas in ordered structures (with Daniel Hoffmann and Jinhe Ye),
arXiv:2004.10953, Israel Journal of Mathematics 254 (1), 293-312.
A family of dp-minimal expansions of (Z; +) (with Erik Walsberg), arXiv:1711.04390, Notre Dame Journal of Formal Logic 64 (2), 225-238.
Semialgebraic method and generalized sum-product phenomena (with Yifan Jing and Souktik Roy), arXiv:1910.04904, Discrete Analysis, https://doi.org/10.19086/da.55555. Talk.
Zarankiewicz’s problem for semilinear hypergraphs (with Abdul Basit, Artem Chernikov, Sergei Starchenko, and Terence Tao), arXiv:2009.02922, Forum of Mathematics, Sigma, volume 9, 2021. Basit’s Talk.
Interpolative fusions (with Alex Kruckman and Erik Walsberg), arXiv:1811.06108,
Journal of Mathematical Logic. 2020 Nov 28:2150010.
The additive groups of Z and Q with predicates for being square-free (with Neer Bhardwaj), arXiv:1707.00096, The Journal of Symbolic Logic, vol. 85 (2020).
Preprints
On the shatter function of semilinear set systems (with Abdul Basit), arXiv: 2501.10032, 2025
Measure doubling in unimodular locally compact groups and quotients, (with Zuxiang Kong, and Fei Peng), arXiv:2411.17246, 2024
Measure doubling of small sets in SO(3,R) (with Yifan Jing and Ruixiang Zhang), arXiv:2304.09619, 2023, Yifan’s Talk
Interpolative fusions II: Preservation results (with Alex Kruckman and Erik Walsberg), arXiv:2201.03534, 2022
Measure growth in compact semisimple Lie groups and the Kemperman Inverse Problem (with Yifan Jing), arXiv:2303.15628, 2023. Yifan’s Talk.
(Formerly, Minimal and nearly minimal measure expansions in connected unimodular groups (with Yifan Jing), arXiv:2006.01824)
Tame structures via multiplicative character sums on varieties over finite fields, arXiv:1704.03853, 2017
Algebraically Closed Fields with a Generic Multiplicative Character (with Tigran Hakobyan), arXiv:1705.00261, 2017
Coauthors: Jinpeng An, Abdul Basit (2), Neer Bhardwaj, Benjamin Castle, Artem Chernikov, Tigran Hakobyan, Daniel Hoffmann, Zuxiang Kong, Alex Kruckman (2), Yifan Jing (6), Will Johnson, Fei Peng, Souktik Roy, Sergei Starchenko, Terence Tao, Ruixiang Zhang (3), Erik Walsberg (4), Jinhe Ye (2).