Welcome!
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
(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 onedimensional differential dynamics remotely with professor
Juan RiveraLetelier.
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 ZhangZagier Height. The study formed my
undergraduate honor thesis
supervised by professor
Juan RiveraLetelier.
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
Conferences Attended
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  MATHUA.0121 Calculus 1 Recitation Leader
 Fall 2020  MATHUA.0121 Calculus 1 Recitation Leader
 Spring 2019  MATHUA.0121 Calculus 1 Recitation Leader
 Fall 2019  MATHUA.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:

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.

The whole website is also a coding project of mine. I learnt all these languages from online materails and
the Youtube Channel
Bro Code.

The domain and hosting service are provided by
Interserver.net. I use
FileZilla as my file transfer protocol (FTP).

Enabling mathematical writings (like using LATEX) in this website is made possible by
MathJax.

Seperate acknowledgements will be given in relevant webpages if necessary.