Hello! I'm Xinyuan Xie. I am doing my PhD with Prof. Paata Ivanisvili at UC Irvine.
My research focuses on proving sharp inequalities in high-dimensional discrete and continuous spaces, at the intersection of probability, analysis, and convex and discrete geometry. These questions, with their simplicity of description and the depth and richness they encode, also arise naturally in combinatorial optimization, computational complexity, and even in modeling how our brains work and remember things.
Email: xinyuax7@uci.edu
Before starting my PhD, I completed my undergraduate at the University of Science and Technology Beijing in 2022 where I did my thesis with Prof. Weifeng Zhao.
Papers
- A simple and efficient curved boundary scheme of the lattice Boltzmann method for Robin boundary conditions of convection–diffusion equations, with Weifeng Zhao and Ping Lin. Applied Mathematics Letters (2021).
- Jackson's inequality on the hypercube, with Paata Ivanisvili and Roman Vershynin (2024).
- Counterexample to majority optimality in NICD with erasures, with Paata Ivanisvili (2025). Invited presentation at STOC 2026 AI + TCS Day.
- Sharp isoperimetric inequalities on the Hamming cube II: The critical exponent, with Polona Durcik, Paata Ivanisvili, and Joris Roos (2026).
- Grokability in five inequalities, with Paata Ivanisvili (2026).
- Sharp log-Sobolev inequalities and quartic stability on finite cyclic groups, with Haonan Zhang (2026).
- Sharp hypercontractivity for free group von Neumann algebras, with Haonan Zhang (2026).
- A Beckmann boundary form of Talagrand's conjecture on the discrete cube, with Paata Ivanisvili and Haonan Zhang (2026).
- The König constant is one, with Haonan Zhang (2026).
- Boolean threshold functions, neuron capacity, and memory retrieval (2026).
- Stability of Szarek's inequality with best constant (2026).