Liu Zhang Program in Applied and Computational Mathematics Princeton University

I am a PhD student in Applied Mathematics at Princeton University, where I am very fortunate to be advised by Amit Singer and co-advised by Charles Fefferman. Previously, I graduated summa cum laude from Yale-NUS College in Singapore, majoring in Mathematical, Computational, Statistical Sciences (MCS) with a focus area in Mathematics. I was a recipient of the Outstanding Capstone Project in MCS, the college's graduation award for the best honors thesis in the major.

Research Interests.

• Tensor methods.
• Manifold learning.
• Dimensionality reduction.

Projects and Manuscripts.

• (B.Sc. Honors Thesis) Manifold Structure of Artificial and Biological Neural Networks
  Thesis advisors: Steven W. Zucker, Francesca Spagnuolo, Luciano Dyballa
• Improving Deep Neural Network Training Using Sobolev Loss Functions (poster)
  with Aparna Gupte, Yunan Yang, Alex Townsend
  Joint Mathematics Meetings PME Poster Session 2022
• Analytic-Geometric Asymptotic Analysis of Exponential Polynomials (code, pdf)
  with David A. Smith
• Asymptotic Locus of Zeros of Exponential Sums and Julia Library for Exponential Sums (code, pdf)
  with David A. Smith
• Formal Verification of Interpreter, Compiler, Virtual Machine for Arithmetic Expressions (code, pdf)
  with Olivier Danvy