About Me
Hi, I’m Alex! Currently I’m in the process of transitioning from academic to ML engineering–check out some of my projects on Github.
I recently wrapped up my PhD in mathematics at Columbia University, where I was fortunate to be advised by Prof. Francesco Lin. During my PhD, I worked on low dimensional topology, differential geometry, and gauge theory. Specifically, I thought about the Seiberg–Witten equations and their interactions with Einstein metrics. Before that, I did my undergrad at UC Santa Barbara, and did my undergraduate thesis under the supervision of Prof. Xianzhe Dai.
Outside of work, I enjoy bouldering, brewing specialty coffee and tea, baking bread, and cooking. I also enjoy playing Pokemon Go.
If you want to contact me, send an email to axu930 (at) gmail.com and I’ll do my best to get back to you. In the meatime, feel free to check out my resume below. Or view it as a PDF.
Skills
- Programming Languages: Python, Java, C/C++, Rust, PyTorch, Scikit-learn, Numpy, Pandas, Polars, SQL, LaTeX
- Mathematics & Statistics: Bayesian Statistics, Variational Inference, Convex Optimization, Linear Regression, Partial Differential Equations, Differential Geometry, Riemannian Manifolds
- Machine Learning: Variational Autoencoders, Diffusion Models, Transformers, Retrieval Augmented Generation, Low Rank Adaption
- Languages: Native proficiency in English and Chinese
Experience
- Instructor of Record for Calculus 1. Created course curriculum and taught biweekly 30 student classes
- Graduate TA for Calculus and Optimization, Linear Algebra, Calculus 1, 2, 3, and Algebraic Topology
Education
- Advisor: Prof. Francesco Lin
- Thesis: The Seiberg—Witten Equations and Asymptotically Hyperbolic Einstein Metrics
- Advisor: Prof. Francesco Lin
- Advisor: Prof. Xianzhe Dai
- Thesis: Adiabatic Limits and Hodge Leray Theory
Projects
localRAG
- Implemented retrieval augmented generation (RAG) for a local collection of academic texts using open source models
mini-diffusion
- Implemented a tiny (825k) parameter U-net diffusion model in PyTorch for generation of self-portraits.
LoRA_gpt2
- Implemented low-rank adaption (LoRA) fine tuning on the GPT2 124M checkpoint in PyTorch to generate text in the style of different authors.
VAEs
- Implementation of a variational autoencoder (VAE) to learn the MNIST dataset.
Publications and Preprints
- Seiberg-Witten Equations and Einstein Metrics on Finite Volume 4-Manifolds with Asymptotically Hyperbolic Ends (https://arxiv.org/abs/2402.1036)