Hello, I am Guo-Dong Hong!
Welcome to my website!
I am now a final-year math PhD student at Caltech.
My advisor is David Conlon.
I am applying for postdoctoral positions starting in Fall 2026.
Email: ghong[at]caltech.edu (replace [at] with the appropriate symbol)
Research Interests
My research lies at the intersection of additive combinatorics and arithmetic Ramsey theory, especially where these subjects interact with higher-order Fourier analysis, harmonic analysis, ergodic theory, and geometric measure theory. A guiding principle of Ramsey theory is that a sufficiently large set must contain prescribed structure. My work investigates this principle in several arithmetic and geometric settings, seeking to understand how different notions of largeness force arithmetic or geometric structure.
Research
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- Simultaneous popular polynomial differences over finite fields, with David Conlon and Dingding Dong
- Peres-Schlag’s nonempty-interior problem and a shifted-product variant for product sets, with Chong-Wei Liang and Chun-Yen Shen
- On the Peres-Schlag orthogonal projection problem and Kakeya-type sets, with Chong-Wei Liang and Chun-Yen Shen.
- On weighted multilinear polynomial averages in finite fields
- Polynomial Szemerédi for sets with large Hausdorff dimension on the Torus
- Three-term rational function progressions in finite fields, with Zi Li Lim, Int. Math. Res. Not. IMRN 10 (2025)
Expository
- A study guide for “On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane” after T. Orponen and P. Shmerkin, with Jacob B. Fiedler, Donggeun Ryou, Shukun Wu
