Likun Xie

E-mail: xie@mpim-bonn.mpg.de

I am a postdoctoral fellow at the Max Planck Institute for Mathematics in Bonn. I graduated from University of Illinois Urbana–Champaign in May 2025. I work in number theory and commutative algebra. Currently, I am interested in: arithmetic over function fields; homological conjectures and local cohomology in commutative algebra.

Research

On an Instance of the Small Cohen–Macaulay Conjecture II (2026). To appear in Bull. Lond. Math. Soc. arXiv poster

Products of Prime Ideals in Ray Class Groups (2026). arXiv

Connectedness in Codimension One and the Non-S₂ Locus (2026). arXiv

On a Conjecture of Erdős over Function Fields (2025). Mathematische Zeitschrift. Journal arXiv

Notes

We expect to extend the results to general global function fields beyond the current genus-zero setting. Generalized Jacobians together with the equidistribution framework mentioned in Remark 4.3 are likely to provide a natural setting for such extension.

Almost Prime Orders of Elliptic Curves modulo Prime Powers (2025). arXiv

(with K. Nath) Almost primes and primes that are sums of two squares plus one (2024). Acta Arithmetica. Journal arXiv

On an Instance of the Small Cohen–Macaulay Conjecture (2023). Journal of Pure and Applied Algebra. Journal arXiv

(with B. C. Berndt and A. Zaharescu) Proofs of McIntosh’s Conjecture on Franel Integrals and Two Generalizations (2022). Advances in Mathematics. Journal arXiv