*Singular vectors and psi-Dirichlet numbers over function field, joint with Yewei Xu: to appear in Journal de Théorie des Nombres de Bordeaux. arXiv.
*Winning of inhomogeneous bad for curves, joint with Liyang Shao: Mathematische Annalen Volume 391, pages 4037–4061, (2025). arXiv.
Rectangular shrinking targets for Z^m actions on tori: well and badly approximable systems, joint with Victor Beresnevich and Anish Ghosh and Benjamin Ward: to appear in Acta Arithmetica. arXiv.
Good functions, measures, and the Kleinbock-Tomanov conjecture, joint with Victor Beresnevich and Anish Ghosh: Journal für die Reine und Angewandte Mathematik. [Crelle's Journal], vol. 2024, no. 815, 2024, pp. 71-106. arXiv.
*On absolutely friendly measures on Q_S^d, joint with Justin Liu: Mathematika 70 (2024), no.3, Paper No. e12256. arXiv.
Quantitative Khintchine in simultaneous approximation, Discrete Contin. Dyn. Syst. 44 (2024), no.2, 365–377. arXiv. (appeared in the Editor's choice; see link)
Singular vectors on manifolds over totally real number fields, joint with M.M.Radhika, Monatsh. Math. 200 (2023), no.3, 545–568. arXiv.
Multiplicative p-adic metric Diophantine approximation on manifolds and dichotomy of exponents, joint with Anish Ghosh: Bull. Soc. Math. France 148 (2020), no.4, 733–747. arXiv.
Diophantine inheritance for p-adic measures, joint with Anish Ghosh: Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 23 (2022), no.1, 49–80. arXiv.
S-arithmetic Inhomogeneous Diophantine approximation on manifolds, joint with Anish Ghosh: Adv. Math. 400 (2022), Paper No. 108239, 46 pp.; arXiv.
Winning and nullity of inhomogeneous bad, joint with Liyang Shao. submitted. arXiv.
Rational points near manifolds and Khintchine theorem, joint with Victor Beresnevich. submitted. arXiv.
On weighted singular vectors for multiple weights, joint with Nattalie Tamam. submitted. arXiv.
On Fourier Asymptotics and Effective Equidistribution, joint with Subhajit Jana. submitted. arXiv.
Bad is null, joint with Victor Beresnevich, Anish Ghosh, and Benjamin Ward. submitted. arXiv.
*Singular vectors in real affine subspaces, joint with Yewei Xu. submitted. arXiv.
*-ed items are research with undergraduates.
Good functions, measures, and the Kleinbock-Tomanov conjecture: Talk video (IAS), Talk video (ICTS, ETDS Program), Talk video (NEDNT).
Singular vectors in real affine subspaces: Talk video (Online Seminar in Diophantine Approximation and Related Topics)
Bad is null: Talk video (NEDNT)
Winning of bad: Talk Video (OSU Dynamics)
Fourier Asymptotics and Effective Equidistribution, Talk video (NEDNT), Talk video (UCSD group action)
Justin Liu
M.M Radhika
Benjamin Ward
Yewei Xu