Welcome to Xiyuan's website!
I like to think about problems in number theory, algebraic geometry, and algebraic topology. Currently, I am working on projects related to the following topics.
Serre weight conjectures.
Arithmetic of algebraic varieties.
Rational homotopy theory.
Publications and preprints
Warning: The papers posted on the arXiv may differ from the published versions! I will solve this problem in the future!
Weight elimination in two dimensions when p=2. Mathematical Research Letters (to appear). [arXiv]
Integral Sullivan theory. (with Jonathan Scott and Donald Stanley)
Automorphic Forms and Representation Theory Seminar, Purdue University. Jan. 2021
Junior Number Theory Days, Johns Hopkins University. Dec. 2020
Junior Colloquium, Johns Hopkins University. Nov. 2020
Colloquium, Capital Normal University. Nov. 2020
Peking Online International Number Theory Seminar, Beijing University. May. 2020 [slide]
Algebra Seminar, University of Pennsylvania. Feb. 2020
FRAGMENT Seminar, Colorado State University. Nov. 2019