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Welcome to my personal website! Here is the definition of me.
I'm Xiang Li 李想, a math PhD student of algebra and number theory in the University of Edinburgh working with Prof. Minhyong Kim since 2023. My interests are in algebraic number theory and arithmetic geometry. To be more specific, I am interested in non-abelian Chabauty methods, which provide an efficient way to find rational points on a curve.
Am I the first person coming up with an idea to make the personal website look like a math book that contains definition/remark etc.?
CV
You can find my detailed CV (curriculum vitae) by clicking here. Below is my education background.
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Sep 2023 – Now
PhD in Mathematics
The University of Edinburgh, School of Mathematics (Hodge Institute)
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Oct 2022 – Jun 2023
MASt in Mathematics
University of Cambridge, Department of Pure Mathematics and Mathematical Statistics
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Sep 2020 – May 2022
BSc in Mathematics
The University of Edinburgh, School of Mathematics
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Sep 2018 – Jun 2020
BSc in Mathematics
South China University of Technology, School of Mathematics
Research
Recent Research Interests
With Martin Lüdtke, we are extending the Chabauty-Kim method for the thrice-punctured line to number fields, in particular cyclotomic fields. We can show that Kim's Conjecture holds for \(\mathbb{Z}[\zeta_3]\)-points but the polylogarithmic quotient is insufficient to prove Kim's Conjecture for integral points over imaginary quadratic fields different from \(\mathbb{Q}[\zeta_3]\).
Publications
Reports of Projects
Talks
S-integral Points on the Thrice-punctured Line over Cyclotomic Fields
Rigid Geometry and Coleman Function
Introduction to Chabauty-Kim Methods on S-unit Equations
Tannakian Category, Unipotent Completion, and de Rham Fundamental Group
Examples Showcase at GlaMS
Euler's Totient Theorem and the Prime Number Theorem
(with Ella Yu) — Seminar of London Learning Lean. Watch the recording here. See the slides here.
Travel
- Seventeenth Algorithmic Number Theory Symposium 6 Jul – 10 Jul 2026 · Bernoulli Institute, Netherlands
- ChaBONNty Conference 29 Jun – 3 Jul 2026 · Max Planck Institute for Mathematics, Germany
- Young Researchers in Algebraic Number Theory VII 3 Sep – 5 Sep 2025 · University of Nottingham, UK
- The GEARS seminar 7 Feb 2025 · University of Glasgow, UK
- Arithmetic, Geometry, Space and Time: A workshop on the occasion of Minhyong Kim's 61st birthday 25 – 29 Nov 2024 · ICMS, Edinburgh, UK
- Young Researchers in Algebraic Number Theory VI 31 Jul – 2 Aug 2024 · University of Oxford, UK
- The Mordell conjecture 100 years later 8 – 12 Jul 2024 · MIT, US
- Gauge Fields in Arithmetic, Topology and Physics 15 – 19 Apr 2024 · ICMS, Edinburgh, UK
- Winter Workshop Chabauty-Kim 2024 14 – 16 Feb 2024 · Heidelberg University, Germany
Teaching
Current Tutoring
Past Tutoring
Also, I am a tutor for the MathsBase.
Codes
\(L\exists \forall N\)
LEAN is a proof assistant, which allows people to write the proof of theorems in a computer programme language. See the website of LEAN community.
A team of me, Huajian Xin, Ella Yu and others attempted to prove the prime number theorem on LEAN. See our Github repository. Ella Yu and I gave a talk about this project on a seminar of London Learning Lean held by Imperial College. Watch the recording here. See the slides here.
Numerical Library of Mathematics Algorithm
I made a simple C++ library for numerical algorithms such as solving linear systems, integrals, differential equations and so on numerically. See my Github repository.