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).

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.

Publications

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

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