My personal website 我的个人主页: https://lambdacdm.github.io/home

My CV (this webpage) 我的个人简历（此页面）: https://lambdacdm.github.io/homepage/

Xiang Li 李想

I’m Xiang Li 李想, a first year math PhD student of algebra and number theory in the University of Edinburgh working with Prof. Minhyong Kim. 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.

Email   s2132101@ed.ac.uk

Address(working)   Bayes Centre, the University of Edinburgh

Education

• Sep 2023 - Now (PhD) The University of Edinburgh (UoE) School of Mathematics (Hodge Institute)

• Oct 2022 - Jun 2023 (MASt) University of Cambridge (Cam) Department of Pure Mathematics and Mathematical Statistics

• Sep 2020 - May 2022 (BSc) The University of Edinburgh (UoE) School of Mathematics

• Sep 2018 - Jun 2020 (BSc) South China University of Technology (SCUT) School of Mathematics

Recent Activities

I have attended / will attend the following conferences.

• 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 July - 2 Aug 2024, University of Oxford, UK

• The Mordell conjecture 100 years later 8 - 12 July 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

Experience

• May 2023 The Modularity Theorem and the Modular Approach (Cam)

  Supervisor: Dr. Hanneke Wiersema

  Abstract: The goal of the essay is to show how the modularity theorem implies Fermat’s Last Theorem (FLT). We begin the essay by discussing about elliptic curves, modular forms and their Galois representations. Then we state the modularity theorem and Ribet’s level lowering theorem. Next we study the properties of the Frey curve and its representations, and apply those theorems to deduce FLT. Finally we make a short introduction on a general version of modularity theorem.

  Report: Click Here

• Sep 2021 - Mar 2022 Group Project in Algebraic Geometry (UoE)

  Supervisor: Prof. Ivan Cheltsov

  Abstract: In this report we study smooth three dimensional hypersurfaces in P²×P² of bidegree (1,2). We show, via a detailed study of cubic curves, that, under generality conditions, these hypersurfaces (and therefore nets of conics) can be put into one of three standard forms by linear change of coordinates.

  Report: Click Here

Awards

• Aug 2021 Arthur Erdélyi Prize (UoE)

  Up to three prizes, awarded on the basis of distinguished performance in the Degree Examination for Mathematics 3

• Aug 2021 Dr Nigel Suess Prize (UoE)

  awarded on the basis of distinguished performance in the course “Introduction to Number Theory”