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1. Probability theory, stochastic processes and applications : Random walks in Random environment and Point Processes and Hawkes Processes.

2. Financial mathematics: Ruin probability and Actuarial Science and Hawkes process with application to finance/insurance.

3. Data analysis and clustering with Hawkes processes and machine learning with stochastic processes. AI with medical science.

4. Integral inequalities, Fractional inequalities, Quantum inequalities, Fractal-Fractional inequalities, and their applications.

5. Theoretic machine learning algorithm: convergence rate for stochastic gradient descent(SGD) or stochastic optimization algorithms.