I am an undergraduate student at the School of Mathematics, Sun Yat-sen University, advised by Associate Professor Yirong Huang, Associate Professor Yujun Lian, and Professor Changzheng Li. My current work focuses on AI agents, structured decision support, world models, financial AI, and time-series forecasting, alongside Schubert calculus.
I am particularly interested in the following questions:
- How to design simple yet effective forecasting models in data‑scarce financial environments (such as the SRM model we recently completed);
- How to build world models for financial markets—we are trying to introduce world models into finance, but due to severe partial observability and non-stationarity in financial systems, the results are not yet satisfactory and we are still exploring;
- How to develop agent systems that are robust, explainable, and trustworthy, and that provide structured and auditable support for financial decision‑making—my advisors and I are very interested in this direction, but progress has been limited so far.
Ultimately, these directions converge on the same core question: how to obtain good forecasts, and how to make good decisions based on those forecasts.
In addition, I maintain an interest in algebraic geometry, particularly Schubert calculus, and I follow geometric learning on Grassmannian manifolds. So far, applications of Schubert calculus in machine learning are extremely rare; only a few studies have attempted to use Schubert varieties as trainable prototypes for subspace clustering. I hope to explore broader uses of Schubert calculus in machine learning algorithms in the future.
Research interests
- AI agents
- Structured decision support
- World models
- Financial AI
- Time-series forecasting
This project studies geometric similarity between historical volatility paths and its use in nonparametric realized-volatility forecasting.
This is an extension of the previous shape‑based forecasting work—it wraps the SRM model with an auditable interface that parses structured forecasting requests, checks the information boundary, retrieves geometric analog paths, and saves complete audit records. The research design and system specification are mine.
This project studies a post-processing layer for volatility forecasts, with the aim of reducing the frequency and magnitude of underestimation without redesigning the underlying forecasting model.
This is a very rough model and is still being improved.
Joint work with Yihua Yue. This project studies positivity phenomena for quantum double Schubert polynomials and develops a proof-oriented treatment of the relevant geometric and combinatorial structures.
Contact: tongrenxiao7@gmail.com · website