intro
Hy P.G. Lam
I obtained my PhD in Mathematics from Northwestern University. My primary research interest lies at the interface of spectral geometry and dynamical systems, focusing on the spectral and dynamical invariants arising in inverse spectral theory. I studied under the late Steve Zelditch and later worked independently with partial guidance and morale support from Jared Wunsch and Elton Pei Hsu. The premise of my thesis and ongoing research endeavors centers on the spectral analysis of unitary operators within the framework of Koopman-von Neumann mechanics, exploring the connections between classical integrable systems, ergodic theory, and quantum mechanics. A key aspect of this work involves studying the Koopman operator of geodesic flows on unit phase spaces of compact Riemannian manifolds and developing the associated inverse-spectral theoretic framework of the underlying geometries.
Email: hylam.math@gmail.com
Curriculum vitae
Research statement
Please email me to request a draft of my dissertation.
Papers
- Heat-kernel method for computing flat-trace distribution on surfaces of revolution - in preparation
- Koopman dynamics on Heisenberg manifolds - in preparation
- Rigidity of flat traces on negatively curved compact 2-manifolds - in preparation
- Flat trace distribution of the geodesic flow on compact hyperbolic plane — arXiv
- Non-isometric pairs of Riemannian manifolds with the same Guillemin-Ruelle zeta function — arXiv (submitted to Journal of Spectral Theory)
- The Replacement Property of PSL(2,p) and PSL(2,p^2) — arXiv
Teaching
Courses I have taught as a graduate teaching assistant and/or served as a non-profit private mentor:
- MATH 218-2 (Single-Variable Calculus with Precalculus) - Fall 2019, Spring 2024
- MATH 220-1,2 (Single Variable Differential Calculus) - Fall 2019, Fall 2021
- MATH 240 (Linear Algebra) - Winter 2021
- MATH 320-2,3 (Real Analysis Upper-Division Sequence) - Winter 2022
- MATH 314 (Probability and Statistics for Econometrics) - Fall 2020, Fall 2023
- MATH 382 (Complex Analysis for ISP) - Winter 2022
- MATH 366-1 (Mathematical Models in Finance) - Winter 2024
- MATH 450-1,2,3 (Probability Theory and Stochastic Analysis, Graduate Sequence) - Fall 2020, Winter 2021, Fall 2021, Winter 2022, Fall 2023, Winter 2024
Courses I have served as a private tutor and/or grader:
- MATH 202-0 (Finite Mathematics)
- MATH 218-1 (Single Variable Calculus)
- MATH 230-1 (Multivariable Differential Calculus)
- MATH 290 (Linear Algebra and Multivariable Calculus)
- MATH 321-1,2,3 (MENU: Real Analysis)
- MATH 311-2 (MENU: Probability and Stochastic Processes)
- MECS 560-1,2 (Static/Dynamics Optimization in Economics)
- MATH 445-1,2 (Graduate Sequence in Differential Geometry)
Directed Reading Projects
- I mentored advanced undergraduate students on topics related to dynamical systems, functional analysis, and quantum theory (most recent project discussed Hamiltonian mechanics).
Data Science/ML Projects
- Sentiment Analysis and Stock Dynamics:
A team-based data science research project where we gathered and analyzed text data from over 600+ news articles on the top 20 publicly-traded companies to assess market impact. Evaluated and ranked 4 predictive models (Sentiment Analysis - VADER, Linear Regression - LinReg, Spearman Correlation, and ARIMA/ARIMAX) in their forecasting performance on volatility parameters, including traded stock volume, high/low, and close prices.
Hobbies
- I enjoy practicing martial arts (kickboxing) and playing chess board games (chess and xiangqi).