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Hi, I'm a final year math master student at Universität Bonn.
I'll be a PhD student at University of Pittsburgh this Fall.
During Sep 22 - Oct 3, I'll be back to Bonn for short research stay and travel to Essen for Kleine AG.
In Spring 2026, I'm expected to be on leave and visiting Bonn, Padova, and École Polytechnique.
Then I'll return to Pittsburgh for Summer 2026 (until when my affiliation with Bonn will be kept).
Email: xiao [at] uni-bonn [dot] de & hax87 [at] pitt [dot] edu
I'm interested in arithmetic geometry and representation theory.
I'm currently writing my master thesis on spherical varieties and geometric Satake supervised by Dr. Arnaud Eteve (with Prof. Dr. Jessica Fintzen as my formal advisor).
Previously, I've worked on mathematical/theoretical/computational physics.
This semester's Kleine AG on Mazur's torsion theorem will be held at Essen by Save.
Last semester's Kleine AG on Shimura varieties was held at Bonn by my friend Dave.
Publications/Preprints/Writings
Publications/Preprints/Writings
Research Papers
Spherical varieties and geometric Satake (in preparation)
Characterizations of sharp solute-solvent interfaces in hydrophobic environments via cylindrical coordinates arxiv.org/abs/2412.13590
A new counterexample to Nguyen’s conjecture on surface fibration (with Wenyi Cai, Yuanyuan Qian, and Lingyu Zhuo) arxiv.org/abs/1811.10421
Mathematical Translation
English SGA4½ Étale Cohomology EnglishSGA4.5
Lecture Notes & Expository
Introduction to Deligne-Lusztig theory (Ongoing)
Representations of compact Lie groups (Ongoing)
Rigid analytic geometry (Pending)
Local class field theory (Pending)
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