Research

I am fortunate to have had the opportunity to collaborate with Dr. Zhengyan Wu, Dr. Lukas Gräfner and Prof. Nicolas Perkowski. I had the honour of being supervised by Prof. Benjamin Fehrman and Prof. Benjamin Hambly during my time as a PhD student (2021-2025).

Publications

1.  Lukas Gräfner, Nicolas Perkowski, and Shyam Popat. "Energy solutions of singular SPDEs on Hilbert spaces with applications to domains with boundary conditions." Stochastics and Partial Differential Equations: Analysis and Computations (2026): 1-47.

2. Popat, Shyam. "Well-Posedness of the generalised Dean–Kawasaki Equation with correlated noise on bounded domains." Stochastic Processes and their Applications 179 (2025): 104503.

Preprints

1. Shyam Popat and Zhengyan Wu. "Ergodicity for the Dean–Kawasaki Equation with Dirichlet Boundary Conditions: Taming the Square-Root." Submitted.

2. Shyam Popat. "Small noise fluctuations and large deviations of conservative SPDEs with Dirichlet boundary conditions." Submitted.

PhD Thesis

1.  Shyam Popat. "Well-posedness and fluctuations of the Dean–Kawasaki equation with coloured noise on bounded domains." PhD diss., University of Oxford, 2025.