Research

I am fortunate to have had the opportunity to collaborate with Dr. Jae-Hwan Choi, Dr. Ankit Kumar, Andrea Pitrone, Dr. Max Sauerbrey,  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. Jae-Hwan Choi, Ankit Kumar, Andrea Pitrone, Shyam Popat and Max Sauerbrey. "The stochastic Keller--Segel system in critical spaces."  Contribution to the Oberwolfach Report for the Seminar 'Stochastic Partial Differential Equations in Critical Spaces' organized by Antonio Agresti and Mark Veraar. (2026).

2. Shyam Popat and Zhengyan Wu. "Ergodicity for the Dean–Kawasaki Equation with Dirichlet Boundary Conditions: Taming the Square-Root." Submitted. (2025).

3. Shyam Popat. "Small noise fluctuations and large deviations of conservative SPDEs with Dirichlet boundary conditions." Submitted. (2025).

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.