Research & Awards

Research Interests: Probability Theory, Stochastic Differential Equations, Quantitative limit theorems for stochastic systems, e.g., Stochastic Gradient Descent (SGD), Multiscale Diffusions and Controlled Dynamical Systems, Malliavin Calculus: Application of second-order Poincaré inequality, Study of McKean-Vlasov (law dependent) Stochastic Systems through the notion of Lion’s derivative, Gaussian fluctuations for Stochastic Partial Differential Equations (SPDEs).                                                              

Publications

 Published:

• Shivam Singh Dhama, Konstantinos Spiliopoulos. Uniform-in-time bounds for a stochastic hybrid system with fast periodic sampling and small white noise. Stochastics & Dynamics, 25 (1), 2550006, 2025. (arXiv) 

• Shivam Singh Dhama. Asymptotic analysis of dynamical systems driven by Poisson random measures with periodic sampling, SIAM Journal on Multiscale Modeling & Simulation, 23 (2), 959–984, 2025. (arXiv) 

• Shivam Singh Dhama, Chetan D. Pahlajani. Fluctuation analysis for a class of nonlinear systems with fast periodic sampling and small state-dependent white noise, Journal of Differential Equations, 362, 438-483, 2023. (arXiv) 

• Shivam Singh Dhama, Chetan D. Pahlajani. Approximation of linear controlled dynamical systems with small random noise and fast periodic sampling, Mathematical Control & Related Fields, 13 (3), 852-872, 2023. (arXiv) 

• Shivam Singh Dhama, Chetan D. Pahlajani. Asymptotic analysis of discrete-time models for linear control systems with fast random sampling. In 2021, the Seventh Indian Control Conference (ICC), 359–364. IEEE, 2021. (link to article) 

Under review/submitted:

• Solesne Bourguin, Shivam Singh Dhama, Konstantinos Spiliopoulos. Quantitative fluctuation analysis for continuous-time stochastic gradient descent via Malliavin calculus, submitted, 2026. (arxiv) 

• Shivam Singh Dhama. Uniform-in-time Gaussian fluctuations for the nonlinear multiscale stochastic systems via Malliavin calculus, submitted, 2026. (arXiv)

Awards/Academic Achievements

• Awarded (jointly with Chetan D. Pahlajani) the A.K. Agarwal award-2025 of the Indian Mathematical Society (IMS) for the article “Fluctuation analysis for a class of nonlinear systems with fast periodic sampling and small state-dependent white noise” in the 91st IMS conference, Lucknow University, India, Dec 2025.

• Department postdoctoral fellowship, Boston University, USA. July 2023.

• Best student paper award of the Seventh Indian Control Conference, IIT Bombay, 2021, for the article “Asymptotic analysis of discrete-time models for linear control systems with fast random sampling.”

• Qualified Graduate Aptitude Test in Engineering (GATE) for Ph.D. in IITs with All India Rank (AIR) 8.

• Qualified Council of Scientific and Industrial Research (CSIR)-National Eligibility Test (NET) with Junior Research Fellowship (JRF) AIR 20, 61.

• Secured AIR 1 in Haryana Public Service Commission (HPSC) Assistant Professor Exam in Mathematics, 2019.

• One of the recipients of Merit-cum-Means Scholarship at IIT Gandhinagar.

• Secured 2nd rank (CGPA-based) in M.Sc. in the Discipline of Mathematics.

• Silver Medal for being the second in B.Sc.

• Secured 1st (college) and 2nd (district) ranks in Intermediate (12th) U.P. Board Exams.

• Secured 2nd college rank in High School (10th) U.P. Board Exams.