Xianzhi: Portfolio Site

Solving a Saddle Point Problem

Wed, 13 May 2026 11:07:06 -0500

A finite-element saddle-point solver written with deal.II

This post walks through a research/coursework project that I worked on this during spring 2025 semester: a two-component finite-element solver, written in C++ using the deal.II library, for a saddle-point system that arises when one tries to compute the harmonic Riesz representation of a given functional in the dual of $H^1$. The full code documentation lives at saddle-point-project url, it is grown out of the MATH 676 project that I completed in spring 2025.

Tech Notebook: A Machine Learning & Deep Learning Journey

Sat, 03 Jan 2026 22:34:22 -0500

The actual blog (with code) is at: https://xianzhiwang1.github.io/tech-blog/

I maintain a personal technical blog where I write up what I learn as I work through machine learning and deep learning, both inside coursework and on my own. This project grows out of the CS0451 Machine Learning class I took at Middlebury College. The overarching theme of this tech blog is understanding by building: each post takes a single idea, walks through the math behind it, implements it in Python (usually from scratch first, then alongside a library reference), and then puts the implementation to work on a real dataset. The site is built with Quarto and published from a stack of Jupyter notebooks, so every post is a fully reproducible mix of derivations, explanations, code, plots, and embedded source files.

About

Tue, 14 Jan 2025 12:56:23 -0600

My name is Xianzhi Wang. I am a Graduate student in Mathematics at Texas A&M University with a strong foundation in applied mathematics, optimization, and software development. I am passionate about leveraging my analytical skills and programming expertise to solve complex problems in data science and software engineering.

SKILLS

Programming Languages: Python, C++, MATLAB
Technologies & Frameworks: Git, deal.II, ParaView, MOSEK, PyTorch, Docker, NumPy, SymPy, Linux/Ubuntu
Core Competencies: Bayesian Statistics, Minimax Theory, Deep Learning, Machine Learning, Probability Theory, Optimal Recovery, Optimization, Numerical Methods, Finite Element Methods, Algorithm Design

EDUCATION

PhD in Mathematics | Texas A&M University | Expected Spring 2028
Master of Science in Mathematics | Texas A&M University | 2025 | GPA: 3.785
Bachelor of Arts in Mathematics | Middlebury College | Aug 2023 | Summa Cum Laude
Study Abroad | Budapest Semesters in Mathematics | Aug 2021 - Aug 2022 | Highest Honors

EXPERIENCE

Research Assistant | Middlebury College & Budapest Semesters in Mathematics | May 2021 - May 2023

Neovim (Lua) authoring: Packer.nvim, Markdown preview, and TeX Live

Tue, 14 Jan 2025 12:54:45 -0600

Neovim is my primary modal editor for technical writing and lightweight IDE-style tasks. Configuration is expressed in Lua and versioned in this repository. The setup is intentionally incremental: curated plugins, predictable keymaps, and a reproducible local toolchain rather than a monolithic distribution.

Plugin management uses Packer.nvim today; I am evaluating Lazy.nvim for faster startup and declarative spec loading (see below). For Markdown, Alt+k triggers markdown-preview.nvim in an existing browser session—equivalent to :MarkdownPreview—via Packer declarations such as:

Terminal email with Mutt: Gmail, OAuth 2.0, IMAP, and SMTP

Tue, 14 Jan 2025 12:51:24 -0600

This write-up summarizes a CLI-first email stack built around Mutt on Linux, with Google Gmail over IMAP/SMTP and OAuth 2.0 for authentication—relevant when Google Workspace or policy blocks legacy app passwords.

For a personal Gmail account where app passwords remain available, mutt-wizard plus an app password is the fastest path: generate credentials in the Google Account security UI, install the wizard from GitHub, and follow its prompts. That flow assumes comfort with the shell and a working muttrc layout.

Layered keyboard layout with KMonad on Linux (i3)

Tue, 14 Jan 2025 12:48:18 -0600

This note documents how I use KMonad, a cross-platform, user-space keyboard remapping daemon written in Haskell, to implement a layered keymap on a Linux workstation. The configuration lives alongside my window manager setup in this i3 repository.

Compared to QMK/ZMK firmware, KMonad runs in user space on the host OS, which makes it easy to iterate on declarative layout definitions without flashing hardware. The mental model is similar to embedded keymaps: layers, tap-hold behaviors, and modifier chords, expressed as structured configuration rather than ad hoc desktop shortcuts.

Research

Sat, 17 Aug 2024 16:16:13 -0500

Current Research

Solving Poisson equation with incomplete noisy information

Current research project advised by Dr. Andrea Bonito:

Algorithmic Development: Engineered C++ code to implement complex minimization algorithms, utilizing the MOSEK C++ FUSION API for high-performance optimization.
Numerical Experiments: Conducted numerical simulations to validate algorithm accuracy and performance, utilizing ParaView for data visualization, Docker for containerization and tmux for efficient CLI-based workflows.
Software Rigor: Applied best practices in memory safety, debugging, and version control to ensure the reliability of mathematical software.
Theory Translation: Translated mathematical frameworks into computationally efficient code, bridging the gap between theoretical research and practical application.

Past Research

Applying Combinatorial Nullstellensatz to no-3-in-a-line problem

Repeatedly applying the Combinatorial Nullstellensatz for Zero-sum Grids to Martin Gardner’s minimum no-3-in-a-line problem
Published Version: https://doi.org/10.1016/j.ejc.2024.104095;
ArXiv Link:
https://arxiv.org/abs/2401.03119;\

Teaching Assistantship

Sat, 17 Aug 2024 16:15:51 -0500

Teaching Experience

Spring 2026

Fall 2025

Spring 2025

Teaching Assistant for Math 151, Engineering Mathematics I, lead weekly labs and recitation sections.

Fall 2024

Teaching Assistant for Math 151, Engineering Mathematics I, lead weekly labs and recitation sections.

Summer 2024

Grader for Undergraduate Linear Algebra Course at TAMU.

Spring 2024

Teaching Assistant for Math 152, Engineering Mathematics II, lead weekly labs and recitation sections.

Fall 2023

Teaching Assistant for Math 151, Engineering Mathematics I, lead weekly labs and recitation sections.