Publications
A collection of my research work.
On the Existence and Uniqueness of Solutions to Non-Linear Stochastic Partial Differential Equations
Jane Doe, Jiale Liu, Richard Feynman
Annals of Probability 2025
Mathematical proof of existence and uniqueness for non-linear SPDEs with multiplicative Lévy noise, extending theory to non-Lipschitz coefficients.
A Constructive Proof of the Generalized Riemann Hypothesis for Function Fields over Finite Constants
John Smith, Jiale Liu, Alan Turing
Proceedings of the 2024 International Congress of Mathematicians (ICM) 2024
A constructive proof demonstrating the validity of the Generalized Riemann Hypothesis for function fields using spectral interpretation of the Frobenius automorphism.
Numerical Stability Analysis of High-Order Runge-Kutta Methods in Quantum Dynamics
Jiale Liu, Sarah O'Connor†
Journal of Computational Physics 2024
A rigorous analysis of numerical stability boundaries for high-order Runge-Kutta integrators in the context of time-dependent quantum mechanics.
Monte Carlo Simulations of Phase Transitions in 2D Ising Models on Non-Euclidean Lattices
Charlie Brown, Jiale Liu†
2023 International Conference on Computational Physics (ICCP) 2023
Monte Carlo study revealing mean-field-like phase transitions and critical exponent deviations for Ising models on hyperbolic non-Euclidean lattices.
A survey of android application and malware hardening
Vikas Sihag, Manu Vardhan, Pradeep Singh
Computer Science Review 2021