Faculty

• Dynamical Systems
• Operator Theory
• Applied Harmonic Analysis
• Machine Learning and Deep Learning
• Koopman and Liouville Operator Theory
• Reproducing Kernel Hilbert Spaces (RKHS)
• Kolmogorov–Arnold Networks (KANs)

• Pokhriyal, S., Lata, S., Singh, D. (2022). Multivariate Sub Hardy Hilbert Spaces invariant under the action of n-tuple of Finite Blaschke Factors. Journal of Mathematical Analysis and Applications.

• Pokhriyal, S., Lata, S., Singh, D. (2023). Invariant Subspaces of Powers of Unicellular Operators. New York Journal of Mathematics.

• Fractional-Order Dynamical Control using Kolmogorov-Arnold Networks, with Hongwei Chen, Joel A. Rosenfeld, and Tansel Yucelen.

• Restricted Liouville Operators for the Study of Non-Analytic Dynamics within the Disc, with Joel A. Rosenfeld.

• Integral Formulation of QENDy for Robust Nonlinear System Identification, with Nikhil Saran, Stefan Klus, Rushikhesh Kamalapurkar, and Joel A. Rosenfeld.

• Compressed Liouville Operators for the Study of Non-Analytic Dynamics on RKHS, with Joel A. Rosenfeld.

• Mori-Zwanzig Formalism of Dynamical Systems under the Action of Occupational Kernel, with Chukwuebuka Amagwula and Joel A. Rosenfeld.

• Kernalized Active Subspace, with Joel A. Rosenfeld and Benjamin P. Russo (preprint ready).

• Compressed Liouville Operators over the Paley Wiener Space for System Approximation, with Joel A. Rosenfeld (preprint ready).

• Invited Talk (2 Days Session) – Workshop on Mathematics, Applications in AI and Data Science, Dec 20–21, 2025, Banasthali Vidyapith.

• Session Chair – 41st SEAM, 2025, University of South Florida.

• Presented: "Multivariable Sub Hardy Hilbert Spaces Invariant under the Action of Finite Blaschke Factors", 40th SEAM, University of Florida, 2023.

• Presented: "Invariant Subspaces of Powers of Some Unicellular Operators", Jan 2023, IIT Kanpur.

• Presented: "Invariant Subspaces of Powers of Some Unicellular Operators", NCPMA-RAMAA, May 2022, DST-CIMS, Institute of Science, BHU.

• Focus Program on Analytic Function Spaces and Their Applications, July–Dec 2021, Fields Institute, Canada (Enrolled).

• Presented: "Multivariable Sub Hardy Hilbert Spaces Invariant under the Action of Finite Blaschke Factors", 35th RMSCON, Central University of Rajasthan, 2020.

• AIS Operator Theory, 16–28 Dec 2019, IIT Kanpur (Attended).

• ATM School for Modern Aspects of Function Theory, Operator Theory and Operator Algebras, Dec 2018, ISI Bangalore.

• MAC2283 – Engineering Calculus III (Fall 2023, Spring 2024)

• MAP2302 – Differential Equations (Spring 2024, Fall 2025)

• Dynamical Systems
• Operator Theory
• Harmonic Analysis
• Machine Learning
• Linear Algebra
• Differential Equations
• Calculus

Research Positions

• Postdoctoral Researcher, University of South Florida, Tampa, USA. (Aug 2023 – Aug 2025). Host: Prof. Joel A. Rosenfeld.

• Visiting Scientist, Indian Statistical Institute, Bangalore, India. (Feb – May 2023). Host: Prof. Jaydeb Sarkar.

• Research Assistant, Shiv Nadar University, Greater Noida, India. (Aug – Dec 2022). Host: Prof. Sneh Lata.

Academic Faculty

• Primary Instructor, University of South Florida, Tampa, USA. (Aug 2023 – Aug 2025).

Reviewer Experience

• Complex Analysis and Operator Theory
• Discrete and Continuous Dynamical Systems – Series B
• Indian Journal of Pure and Applied Mathematics

Professional Service

• Session Chair, 41st SEAM, 2025, University of South Florida.