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 surfaces.
Rational homotopy theory.
Publications and preprints
Weight elimination in two dimensions when p=2. Submitted, 2017. [arXiv]
Integral Sullivan theory. (with Jonathan Scott and Donald Stanley) In preparation.
Automorphic Forms and Representation Theory Seminar, Purdue University. Jan. 2021
Junior Number Theory Days, Johns Hopkins University. Dec. 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