Postdoctoral fellow
Dr. Abhishek Chaudhary
Employment#
- Nov 2022 – present: Postdoctoral fellow, Universität Tübingen, Mathematisches Institut. Mentor: Prof. Andreas Prohl
- Sep 2022 – Oct 2022: Postdoctoral fellow, TIFR, Centre for Applicable Mathematics, Bangalore, India. Supervisor: Prof. Ujjwal Koley
Academic profile#
- Aug 2018 – Aug 2022: PhD research scholar, TIFR, Centre for Applicable Mathematics, Bangalore, India. Thesis advisor: Prof. Ujjwal Koley. Thesis title: On kinetic and measure-valued solutions to fluid flow equations.
- 2016 – 2018: M.Sc. in Mathematics, TIFR, Centre for Applicable Mathematics. University: Tata Institute of Fundamental Research, Mumbai. Marks: 80.25%.
- 2013 – 2016: B.Sc. (Honours) in Mathematics, Deen Dayal Upadhyaya College, University of Delhi. Marks: 91.67%.
Research interests#
- Stochastic partial differential equations (SPDEs)
- Stochastic conservation laws
- Numerical analysis
- Stochastic optimal control problems
- Regularization effect of noise
- Statistical learning
- Machine learning
Selected publications and research works#
Preprints#
A. Chaudhary, U. Koley, A. Prohl, Convergence of a fully discrete approximation for the stochastic 2D Euler equations with Kraichnan transport noise, preprint, 2026.
D. Breit, S. Ranjan Behera, A. Chaudhary, Error analysis for 3D Navier–Stokes equations with additive noise, preprint, 2026.
L. Banas, D. Breit, A. Chaudhary, A. Prohl, A higher order discretization for the stochastic Navier–Stokes equations with additive noise, preprint, 2026.
Accepted and published articles#
A. Chaudhary, A. Prohl, Higher order numerical schemes for SPDEs with additive noise, IMA Journal of Numerical Analysis, accepted for publication, 2026.
A. Chaudhary, A numerical method to simulate the stochastic linear-quadratic optimal control problem with control constraints in higher dimensions, Numerische Mathematik, 2026.
A. Chaudhary, Convergence analysis for an implementable scheme to solve the linear-quadratic stochastic optimal control problem with stochastic wave equation, Journal of Scientific Computing 108, Article 88 (2026).
A. Chaudhary, U. Koley, E. Wiedemann, Dissipative measure-valued solutions and weak–strong uniqueness for the Euler alignment system, Journal of Evolution Equations 26, Article 7 (2026).
A. Chaudhary, F. Merle, A. Prohl, Y. Wang, An efficient discretization to simulate the solution of linear–quadratic stochastic boundary control problem, IMA Journal of Numerical Analysis, draf060 (2025).
A. Chaudhary, Stochastic fractional conservation laws, J. Math. Anal. Appl. 531 (2024).
A. Chaudhary, Stochastic degenerate fractional conservation laws, Nonlinear Differential Equations and Applications NoDEA 30 (2023), no. 3, Paper No. 42, 48 pp.
A. Chaudhary, G. Vallet, A short remark on inviscid limit of the stochastic Navier–Stokes equations, Z. Angew. Math. Phys. (2023) 74:219.
A. Chaudhary, U. Koley, A convergent finite volume scheme for the stochastic barotropic compressible Euler equations, ESAIM Math. Model. Numer. Anal. 57 (2023), no. 6.
A. Chaudhary, U. Koley, On weak-strong uniqueness for stochastic equations of incompressible fluid flow, J. Math. Fluid Mech. 24 (2022), no. 3, Paper No. 62, 33 pp.
A. Chaudhary, Convergence of a spectral method for the stochastic incompressible Euler equations, ESAIM Math. Model. Numer. Anal. 56 (2022), no. 6.
Grants#
- Sep – Oct 2024: Travel grant from University of Tübingen, to participate in the ICTS program on Deterministic and Stochastic Analysis of Euler and Navier–Stokes Equations, Bangalore, India.
- Feb – Mar 2024: Travel grant from University of Tübingen, for a visit to TIFR CAM Bangalore, IIT Delhi, IIT Roorkee, and IIT Ropar, India.
- May 2023: Research grant from University of Tübingen, for a visit to the University of Pau, France.
- July 2022: Research grant from the TIFR CAM fund, to attend the 2nd IST Austria Summer School in Analysis and PDEs, Institute of Science and Technology Austria, Klosterneuburg.
- Feb – Mar 2022: Research grant from the IFCAM project “Evolutionary PDEs: degeneracy, noise and approximations”, for a visit to the University of Pau, France.
Awards and fellowships#
- Nov 2022 – present: Postdoctoral fellowship, University of Tübingen
- Sep 2022 – Oct 2022: Postdoctoral fellowship, Tata Institute of Fundamental Research
- Aug 2018 – Aug 2022: Doctoral fellowship, Tata Institute of Fundamental Research
- July 2016 – July 2018: Master’s fellowship, Tata Institute of Fundamental Research
- 2016: M.Sc. and Int. Ph.D. entrance exams cleared (IIT Guwahati, IISER Bhopal, IISER Mohali, TIFR CAM Bangalore)
- 2013 – 2016: INSPIRE Scholarship for Higher Education, Department of Science and Technology, India
Teaching experience#
- April – July 2026: Teaching, University of Tübingen, Numerical Optimization (3h/week).
- October 2025 – February 2026: Teaching, University of Tübingen, Mathematical Introduction to Data Science (3h/week).
- April – July 2025: Teaching, University of Tübingen, Financial Mathematics and Numerics (3h/week).
- Oct 2024 – Feb 2025: Teaching, University of Tübingen, Numerical Optimization (3h/week).
- April – July 2024: Teaching, University of Tübingen, Optimal Control Theory with ODE and Numerics (3h/week).
- Oct 2023 – Feb 2024: Teaching, University of Tübingen, Stochastic Differential Equations with Numerics (3h/week).
Teaching assistance#
- April – July 2023: University of Tübingen (Prof. Andreas Prohl, Statistical Learning 2). Conducted tutorial classes (2h/week).
- April – July 2023: University of Tübingen (Prof. Andreas Prohl, Statistical Learning 1). Conducted tutorial classes (2h/week).
- November 2022 – February 2023: Teaching guidance, University of Tübingen (Prof. Andreas Prohl, Seminar Statistical Learning 1). Conducted discussions with graduate students to prepare seminar talks (2h/week).
- Feb 2020: TIFR-CAM (Prof. Martina Hofmanová, Stochastic Compressible Fluid Flows). Conducted discussion classes.
- Jan – July 2020: TIFR-CAM (Prof. Ujjwal Koley), Fluid Mechanics. Conducted discussion classes and assigned grades.
- Aug 2019: TIFR-CAM, NCMW – System of Conservation Laws Theory and Numerics, Hyperbolic Conservation Laws. Conducted discussion classes.
- Jan – July 2019: TIFR-CAM (Prof. Ujjwal Koley), Measure Theory. Conducted discussion classes and assigned grades.
- Aug – Dec 2018: TIFR-CAM (Prof. Ujjwal Koley), Probability Theory. Conducted discussion classes and assigned grades.
- May – June 2018: TIFR-CAM, SWM program for undergraduates, Real Analysis, Linear Algebra and Advanced Calculus. Conducted discussion classes.
Invited talks#
- May 2025: ENS de Lyon, France — An efficient, implementable discretization of SLQ problem and convergence with rates
- April 2025: ICMS Edinburgh, U.K. — An efficient, implementable discretization of SLQ problem and convergence with rates
- Sep 2024: IIT Jammu, India — An efficient discretization to simulate the solution of linear-quadratic stochastic boundary control problem
- March 2024: IIT Roorkee, India — An efficient discretization to simulate the solution of linear-quadratic stochastic boundary control problem
- March 2024: IIT Ropar, India — An efficient discretization to simulate the solution of linear-quadratic stochastic boundary control problem
- March 2024: Seminar talk for graduate students, University of Delhi, New Delhi — Linear quadratic optimal control problem and numerical optimization
- March 2024: IIT Delhi, India — An efficient discretization to simulate the solution of linear-quadratic stochastic boundary control problem
- Feb 2024: TIFR CAM, Bangalore — An efficient discretization to simulate the solution of linear-quadratic stochastic boundary control problem
- Feb 2024: Seminar talk, University of Tübingen — Stochastic linear quadratic optimal control problem
- May 2023: Seminar talk, University of Pau, France — Measure-valued solution to incompressible Euler equations with stochastic forcing
Conferences and workshops attended#
- April 2025: ICMS, Edinburgh, U.K. — Numerical Modelling of Nonlinear Stochastic Systems
- Feb 2025: Swiss MAP Research Station, Les Diablerets, Switzerland — Swiss MAP Workshop: Stochastic Equations and Stochastic Dynamics
- Sep 2024: ICTS, Bangalore, India — ICTS program on Deterministic and Stochastic Analysis of Euler and Navier–Stokes Equations
- July 2022: Institute of Science and Technology Austria, Klosterneuburg — 2nd IST Austria Summer School in Analysis and PDEs
- Sep – Dec 2020: IIT Kanpur, IISER Pune, IISER Kolkata, TIFR-CAM — Webinar on PDE and related areas
- Feb 2020: TIFR-CAM, Bangalore — Compact course on mathematical aspects of stochastic compressible fluid flows by Prof. Martina Hofmanová
- Jan – Feb 2019: TIFR-CAM, Bangalore — Compact course on mathematical aspects of Euler equations by Prof. Eduard Feireisl
- May 2018: TIFR-CAM, Bangalore — Compact course on stochastic scalar first-order conservation laws by Prof. Julien Vovelle
- June – July 2017: TIFR-CAM, Bangalore — ATM School: AIS Linear Partial Differential Equations
Advanced courses attended#
- Potential theory by Prof. Kaushik Ramachandran, TIFR-CAM, 2019
- Harmonic analysis by Dr. Ramesh Manna, TIFR-CAM, 2018
- Microlocal analysis by Prof. Venkateswaran P. Krishnan, TIFR-CAM, 2018
- Kinetic theory for scalar conservation laws by Prof. K.T. Joseph, TIFR-CAM, 2018
- $L^p$ theory for elliptic PDEs by Prof. K. Sandeep, TIFR-CAM, 2018
Graduate level courses attended#
Real Analysis · Topology · Linear Algebra · Theory of ODE · Measure and Integration · Functional Analysis · Algebra · Elementary PDE · Complex Analysis · Numerical Analysis · Probability Theory · Advanced PDE I · Computational Methods · Differential Geometry · Mechanics · Advanced PDE II
Peer review activities#
- Reviewer, Stochastics and Partial Differential Equations: Analysis and Computations. Reviewed a paper on a topic related to compressible fluid flow equations (certificate).
- Reviewer, Nonlinear Differential Equations and Applications NoDEA. Reviewed a paper on a topic related to mathematical analysis and SPDEs (certificate).
- Reviewer, Computational Methods in Applied Mathematics (CMAM). Reviewed a paper on a topic related to SPDEs and numerical analysis (certificate).
- Reviewer, Zeitschrift für angewandte Mathematik und Physik. Accepted an invitation to review a paper on a topic related to well-posedness theory for a particular system of SPDEs.