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

A nonabelian Brunn–Minkowski inequality (with Yifan Jing and Ruixiang Zhang), arXiv:2101.07782, 2021, accepted by Geometric and Functional Analysis.  Ruixiang’s Talk.

The etale-open topology and the stable field conjecture (with Will Johnson, Erik Walsberg, and Jinhe Ye), arXiv:2009.02319, accepted by Journal of the European Mathematical Society.  Erik’s Talk.

Stable formulas in ordered structures (with Daniel Hoffmann and Jinhe Ye),
arXiv:2004.10953, accepted by Israel Journal of Mathematics.

A family of dp-minimal expansions of (Z; +) (with Erik Walsberg), arXiv:1711.04390, accepted by Notre Dame Journal of Formal Logic.

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

Mode theory of Complex numbers with polynomial functions (with Benjamin Castle), arxiv:2308.01632, 2023, Talk

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

A Cauchy-Davenport theorem for locally compact groups (with Yifan Jing), arXiv:2106.02924, 2021.

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, Neer Bhardwaj, Benjamin Castle, Artem Chernikov, Tigran Hakobyan, Daniel Hoffmann, Alex Kruckman (2), Yifan Jing (6), Will Johnson, Souktik Roy, Sergei Starchenko, Terence Tao, Ruixiang Zhang (3), Erik Walsberg (4), Jinhe Ye (2).