# Welcome!

General Information Mathematical Database Past Research
Personal Writing Coding Tutorial Online Trading Database

## Shenxiong (Adam) Li

Ph.D. Candidate in Mathematics at the University of Barcelona
My PhD Advisor is Martín Sombra.
I am a member of BGS math community of Catalonian region.

## Education:

• Master of Science in Mathematics, Courant Institute of Mathematical Sciences - New York University, May 2021
• Bachelor of Science in Mathematics, University of Rochester, May 2019
• Bachelor of Arts in Economics, University of Rochester, May 2019
• High Distinction

(From Sep 2014 to July 2016, I was an undergraduate student at China Agricultural University, studying International Finance. I transfered to the U.S. by the end of Spring 2016, and continued my undergraduate study at the University of Rochester as a sophomore in Fall 2016.)

## Research:

During the past several years, I've been working on several different reserach projects to seek my true motivation and interests. They primarily focused on height functions and dynamical systems.

However, in the past year, having seen the fast development of data science and related applied areas, I've developed huge interests in applying mathematics to solve real world problems, and in different coding languages. And I am seeking new opportunities for formal trainings to possibly further my potential in these applied areas.

• For the current Ph.D. study, my research primarily focuses on arithmetic geometry, especially on Arakelov geometry. See the following pages in Mathematical Database for more information about related notions.

• During my master study, I started a project in one-dimensional differential dynamics remotely with professor Juan Rivera-Letelier. In particular, I studied the kneading invariant and kneading map of Fibonacci Polynomials. The study was greatly motivated by computations using Mathematica.
• At the initial stage of this project, I gave two talks to the dynamics working group in the mathematics department at the University of Rochester. I have moved my notes to following page of Mathematical Database.
• The following page of my past research describes details of the motivation, goal and results of this project. In particular, it contains the algorithm and computational files to compute kneading invariants and kneading maps Fibonacci Polynomials.
(The project was a cooperation with Chuanyi Wang when he was an undergraduate student at the University of Rochester. And a part of results from this project constituted his undergraduate honor thesis.)

• My undergraduate research focused on the study of canonical height on the projective plane $$\mathbf{P}^{2}(\overline{\mathbb{Q}})$$ intersecting the line $$x+y+z=0$$. This kind of height is called Zhang-Zagier Height. The study formed my undergraduate honor thesis supervised by professor Juan Rivera-Letelier.
The objective of the study was ambitious. It was to find the essential minimum of such canonical height. The problem of essential minimum is generally considered intricate, and it stands at the center of the study of every type of height functions. We ended up facing perplexing geometric problems. On the other hand, as a secondary gain, we found the density point on the spectrum of such height.
• The research was greatly motivated by the paper Algebraic Numbers Close to Both $$0$$ and $$1$$.
• The problem of essential minimum of even such a "simple" height function is already so interesting and complicated enough that it becomes a "toy project" of my Ph.D. study. With more knowledge from algebraic geometry, my understanding of such canonical height became deeper and more general. I gave two talks in the mathematics department at the University of Rochester about the canonical height and the estimation algorithm of essential minimum.
• I have moved my notes of these two talks, including a full explanation of Zagier's paper, to the following page of Mathematical Database.
• The following page of my past research contains details of the motivation, goal, computational files and results of this research.

## Research Activities:

You can find all my current and past research activities here, including talks I gave and the conferences I attended. Apart from them, I also regularly attended another three seminars:

### Talks Given:

• "Canonical Heights on a Special Line" at the University of Rochester, Dynamical Systems Workgroup, May 24th 2022.
• "Heights on Metrized Line Bundles of Algebraic Varieties" at the University of Rochester, Dynamical Systems Workgroup, May 24th 2022.
• "Kneading Invariants and Maps of Fibonacci Polynomial" at the University of Rochester, Dynamical Systems Workgroup, April 15th 2021.
• "Kneading Invariants and Kneading Maps—A Combinatorial View” at the University of Rochester,Dynamical Systems Workgroup, July 24th 2020.
• "Hofbauer Tower and Kneading Maps—A Geometric View" at the University of Rochester,Dynamical Systems Workgroup, July 16th 2020.
• "On the Spectrum and Essential Minimum of Heights in Projective Plane" at the University of Rochester, Honor Thesis Presentation, April 4th, 2019

## Teaching:

You can find all my current and past teaching activities here. Currently though, I am not having any teaching responsibilities.

### Courant Institute of Mathematical Sciences - New York University

• Spring 2021 - MATH-UA.0121 Calculus 1 Recitation Leader
• Fall 2020 - MATH-UA.0121 Calculus 1 Recitation Leader
• Spring 2019 - MATH-UA.0121 Calculus 1 Recitation Leader
• Fall 2019 - MATH-UA.0009 Algebra And Calculus Recitation Leader

### University of Rochester

• Spring 2019 - MTH 282 Complex Analysis Grader
• Fall 2018 - MTH 235 Linear Algebra Grader
• Spring 2018 - MTH 164 Multivariable Calculus Webwork Teaching Assistant
• Spring 2018 - ECO 231W Econometrics Teaching Assistant
• Fall 2017 - ECO 268 Economics of Globalization Teaching Assistant

## Acknowledgement:

1. This website is created solely by HTML, CSS, and JavaScript, written in the VisualStudio Code. Instead of using a content management system, I found this way the most efficient.
2. The whole website is also a coding project of mine. I learnt all these languages from online materails and the Youtube Channel Bro Code.
3. The domain and hosting service are provided by Interserver.net. I use FileZilla as my file transfer protocol (FTP).
4. Enabling mathematical writings (like using LATEX) in this website is made possible by MathJax.
5. Seperate acknowledgements will be given in relevant webpages if necessary.