My Research Topics for Students

Original Research Topics

1. On Population Protocols, Chemical Reaction Networks, and analog computing. Something along the line of

• LPP Computable Number
• Computing Algebraic Numbers by Generalized Ehrenfest Urns
• Python programming, scientific computing (Symbolic calculation, ODE solving) and visualization skills come handy.

2. Normal number and continued-fraction normality related topic.

Study Topics

The following topics are just topics I am interested in learning more about. Please understand I am not an expert on some of these topics, yet.

Combinatorics Related

1. de Bruijn sequence and perfect necklace This topic requires some work on programming, generating the sequences, graph theory, and automata.

2. Symbolic method and algorithm analysis. For example, analysis of Hashmap.

3. Basics of integer partition and q-analog.

4. Basics of p-adic numbers and its applications.

5. Manim Visualization of some of the above topics.

Algorithms and Complexity

1. Derandomization.

2. AKS algorithms

3. Fast Integer Multiplication

Probability Theory and Stochastic Analysis

1. Martingale in the probability theory setting.
2. Martingale: multiplicative method.

Analog computing

1. A Universal Ordinary Differential Equation.
2. Polynomial Time Corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length
3. Recursive functions and Discrete ODEs

Programming Projects

Note that the existence of this category does not say that other projects do not require programming.

1. martingale (gambling strategies on Cantor Space) visualization. (in Python)