Lecturer NTU 2026 - I joined the School of Mathematics at NTU as a research-active lecturer. My work sits at the interface of probability, functional analysis, mathematical finance, and quantum algorithms.

Current projects have two main strands. The first develops functional-analytic foundations for quantum algorithms, including Schrödingerization, Hamiltonian simulation, and PDE-based approaches. The second studies stochastic averaging-learning dynamics, with directions toward random graphs, interacting particle systems, voter models, and quantum walks.

Prospective PhD students should apply through the department and are encouraged to reach out if their interests align with the areas above. Candidates should be willing to chase epsilons and deltas. An inequality a day will serve you well, line by line. Funding opportunities are expected to expand as the research programme develops. Possible PhD project directions include rigorous statistical mechanics, Schrödingerization methods, voter models, stochastic averaging-learning dynamics and quantum walks. Projects may be algorithmic, probabilistic, or analytic depending on the student’s background.

A strong foundation is critical. Ideal preparation includes at least two of the following three areas:

Probability: Measure-theoretic foundations, stochastic processes, and martingales. You should be comfortable with either continuous models (such as Brownian motion and SDEs) or discrete models (such as Markov chains, random graphs, and interacting particle systems).

Functional Analysis: Banach and Hilbert spaces, operator theory, and exposure to partial differential equations.

Quantum Algorithms: Fluency with Nielsen & Chuang. Familiarity with QSVT, block encoding or Hamiltonian simulation is highly valued.

I look for strength in two of these domains; the third can be cultivated during your PhD. Candidates with exceptional strength in a single area, specifically coming from a Theoretical Computer Science (TCS), Mathematical Physics (MP) or Operations Research (OR) background are also welcome. 

Final Year Projects (NTU Students) 

Research Fellow NTU 2022 - 2025  I worked in Milé Gu's quantum group. The transition to physics had a phase change! I also worked with Patrick Pun. I pursued independent research prior to beginning my lectureship. This independent phase heavily focused on formalising quantum algorithms and simulations. Active projects included a large-scale paper on the quantum simulation of the Heston PDE and work to rigorously ground Schrödingerization using Gelfand triples. A textbook is also being prepared for mathematicians or mathematically minded scientists entering the quantum space.

Postdoctoral Fellow Temasek Labs - SUTD 2019 - 2022 I was a postdoc under Ernest Chong  in ISTD. Our project aim was to bring together aspects of Algebraic Geometry and Commutative Algebra to machine reasoning and general AI. We have a working model of solving AI problems and the first paper appeared in CVPR 2023. Another paper, with a different team, was on using tropical algebra for adapter pruning in neural networks.

Research Interests: Pure probability, functional analysis, quantum algorithms, and algebraic geometry. Generally, I like problems to come from complex dynamical situations and then think about the rigorous theory. I prefer problems that have some randomness and require mathematical formalization. Recently, my focus has shifted heavily toward infinite-dimensional probability and formalizing quantum algorithms (like Schrödingerization). I am also continuing to look at computational algebraic geometry applied to artificial intelligence, with probability always inherent in whatever I do. The process of mastering algebra is ongoing, but still, one day I hope to be called an algebraic probabilist!

Thesis:

1.  Social Learning Models: Deterministic and Probabilistic Aspects.