Dr Panqiu Xia

(he/him)

Publication

• Date
• Type

Research

My research interests include both theoretical and applied probability, with a specific focus on two compelling areas: stochastic partial differential equations (SPDEs), and the theory of chemical reaction networks (CRNs).

• The theory of SPDEs merges classical partial differential equations (PDEs) with random (stochastic) fluctuations. These equations play a pivotal role as stochastic models across diverse scientific domains, including neurophysiology, environmental science, chemical reaction-diffusion, infinite particle systems, and statistical mechanics. 
  
  Two equations I am focusing on include:
  
  • The parabolic Anderson model (PAM), initially introduced by physicist Philip Anderson in 1960’s on the entrapment of electrons in crystals with impurities.
  • The super Brownian motion (sBm, aka. Dawson-Watanabe superprocess), the hydrodynamic limit of a sequence of branching particle systems, involving a non-Lipschitz diffusion coefficient.

For these equations, I am interested in the properties of their solutions, such as existence and uniqueness, moment properties, long-term behaviour, spatial averaging, etc.

• The theory of CRNs serves as a powerful tool for modelling the complex dynamics of real-world (bio)chemical systems. Originating in the early 20th century, it initially engaged chemists and physicists studying simultaneous reactions within a closed system. Over the past half-century, this theory has evolved into a distinct mathematical field, borrowing tools from graph theory, dynamical systems, algebraic geometry, probability theory, and computer science. My research in this area focuses on the explicit formulation of the stationary distributions of stochastically modelled CRNs.

Please refer to my Google Scholar page for a complete list of my publications.

Teaching

Biography

Previous positions

• 2022--2024    Postdoc - Auburn University, Auburn, USA.
• 2020--2022    Postdoc - University of Copenhagen, Copenhagen, Denmark.

Education

• 2020               PhD - University of Kansas, Lawrence, USA.
• 2014               MSc - University of Macau, Macau, China.
• 2011               BSc - Wuhan University, Wuhan, China.

Supervisions

Probability theory, stochastic processes, stochastic analysis