Likun Xie

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

I am a postdoctoral fellow at the Max Planck Institute for Mathematics in Bonn. I completed my Ph.D. at the University of Illinois Urbana–Champaign in May 2025. My research interests are in number theory and commutative algebra. Recently I am interested in geometric approaches to arithmetic problems, and sometimes I also think about homological questions in commutative algebra. CV

Likun Xie

Papers and Preprints

On an Instance of the Small Cohen–Macaulay Conjecture II (2026). pdf | arXiv

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