“Wir müssen wissen, wir werden wissen.” ― David Hilbert

Research Interests

• Mathematical Finance, Rough Volatility, Computational Finance and Machine Learning
• Stochastic Analysis and Stochastic (Partial) Differential Equations
• Rough analysis and its applications

Research Projects

1.Lower Bound for Disconnection of Vacant Set in Loop Percolation

Supervisor: Prof. Dr. Maximilian Nitzschner

June 2023 — May 2024, HKUST

The principal aim of this project is to derive asymptotic lower on the probability that in a certain model of random walk loops on the integer lattice, a macroscopic set is disconnected from infinity by the trace of the loops. We further study the large deviations of the occupation-time field for the loop soup and characterize its supercritical behavior.

Publications and Preprints

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Theses

• (Bachelor’s Degree Thesis) Moderate Deviation of Gaussian Fluctuations for Coulomb Gases at Any Temperature, supervised by Prof. Dr. Fuqing Gao, Winter 2023. [PDF] [Slides]

  In this thesis, I study and introduce the transport-based method introduced by Prof. Serfaty, which is used for obtaining the free energy expansion of Gaussian fluctuation of Coulmob gas in 2020. Then I make use of it to establish the moderate deviation principle for Gaussian fluctuation of d-dimensional Coulomb gases with d ≥ 2.