About Me

CHEN Xiao

My name is CHEN Xiao (陳 嘯). I am currently pursuing a Ph.D. in Mathematics at Tsinghua University under the supervision of Prof. HUANG Yi (黃 意). My research interests include hyperbolic geometry, knot theory, combinatorial topology, and Teichmüller theory.

Beyond mathematics, I am also engaged in research on Chinese dialectology, with a particular focus on the Hangzhou dialect, a subvariety of Wu Chinese.

Email: x-chen20 AT mails DOT tsinghua DOT edu DOT cn

Research & Publications

PREPRINT 2024

Systems of Curves on Non-Orientable Surfaces

THESIS 2020

Undergraduate Thesis: Gauss-Bonnet Theorem for Surfaces and Its Applications (in Chinese)

Talks

Geometric Intersection Complexes

January 2025
Topology Seminar
KAIST, Daejeon

Maximal Systems of Curves on Surfaces

October 2024
Topology & Group Theory Seminar
Vanderbilt University, Nashville

Maximal Systems of Curves

September 2024
GIST Seminar
Boston College, Boston

Maximal Systems of Curves Intersecting Pairwise Once on Non-Orientable Surfaces

April 2024
The 735th Doctoral Academic Forum of Tsinghua University
Tsinghua University, Beijing

Maximal Systems of Intersecting Curves on Surfaces

December 2023
N-KOOK Seminar
Osaka University, Osaka

Maximal Systems of Intersecting Curves on Surfaces

December 2023
Nara Topology Seminar
Nara Women's University, Nara

Seminars

G2T2 Seminar

Beijing 2025-

The G2T2 Seminar is organized by Ph.D. students and postdoctoral researchers at Tsinghua University specializing in geometry and topology, serving as an academic platform for exchange. The name “G2T2” refers to the three major fields of Geometry, Group Theory, and Topology, as well as their interdisciplinary directions. The seminar aims to foster mutual encouragement among young scholars, stimulate academic thinking, and broaden research horizons.

Organizers: Yifei CAI, Xiao CHEN, Diptaishik CHOUDHURY, Qiliang LUO, Tuo SUN, Ivan TELPUKHOVSKIY, and Daxun WANG

Latest Seminar:

Time: June 6, 2025, 10:00 AM
Place: Ningzhai 203
Speaker: Kyle FULLER (Rensselaer Polytechnic Institute)
Title: A Discussion of Goodstein's Theorem and the Kirby-Paris Hydra Theorem
Abstract: We begin by introducing Goodstein's theorem and the Kirby-Paris hydra theorem, two well-known results that are expressible in the language of Peano Arithmetic but are beyond its ability to prove. We then review some relevant background from mathematical logic, including Gödel's incompleteness theorems, Gentzen's result on the consistency of Peano Arithmetic, and transfinite ordinals. Next, we cover a proof of both Goodstein's theorem and the Kirby-Paris hydra theorem. Finally, we discuss a surprising result by Kirby and Paris, who built on the foundational work of Gödel, Gentzen, and others to show that both theorems are unprovable in Peano Arithmetic.

YMSC Topology Seminar

Beijing 2021-

The YMSC Topology Seminar is devoted to frontier topics in topology, geometry, and related fields. It regularly invites scholars from across the mathematical community to share their work and engage in meaningful exchange, with the aim of fostering academic dialogue and broadening intellectual horizons.

Organizers: Weiyan CHEN, Honghao GAO, Yi HUANG, Jianfeng LIN, and Weifeng SUN

Latest Seminar:

Time: June 10, 2025, 10:00 AM
Place: Shuangqing Complex Building A, room C654
Speaker: Andrei B. BOGATYREV (Russian Academy of Sciences)
Title: Enumerative problem for Pell-Abel equation
Abstract: The Pell-Abel (PA) functional equation is the reincarnation of the famous Diophantine equation in the world of polynomials, considered N. H. Abel in 1826. The equation arises in many problems: reduction of Abelian integrals, elliptic billiards, the spectral problem for infinite Jacobi matrices, approximation theory, etc. If the PA equation has a nontrivial solution, then there are infinitely many of them, and all of them are expressed via a primitive solution having a minimum degree. Using graphical techniques, we find the number of connected components in the space of PA equations with the coefficient of a given degree and having a primitive solution of another given degree.