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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 insurance.

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

4. Stochastic partial differential equations and application to financial mathematics and biology.

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