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Postdoctoral fellow

Dr. Abhishek Chaudhary

Google Scholar

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.
  • 2013 – 2016: B.Sc. (Honours) in Mathematics, Deen Dayal Upadhyaya College, University of Delhi.
  • 2012 – 2013: Class XII (Intermediate), Public Inter College, Siyana, Bulandshahr, Uttar Pradesh.
  • 2010 – 2011: Class X (High School), BSGM H.S. School, Siyana, Bulandshahr, Uttar Pradesh.

Research interests#

  • Stochastic partial differential equations (SPDEs)
  • Stochastic conservation laws
  • Numerical analysis
  • Stochastic optimal control problems
  • Regularization effect of noise
  • Statistical learning
  • Machine learning

Computational and mathematical skills#

  • Analytical methods: Weak, kinetic, martingale, and dissipative measure-valued solution concepts; compactness and stability arguments; weak–strong uniqueness; convergence and error analysis.
  • Programming: Python.
  • Numerical PDEs: Finite-element, finite-volume, and spectral discretizations; implicit Euler, midpoint, Crank–Nicolson, splitting, projection, and higher-order time-stepping methods.
  • Optimization: Discrete state and adjoint equations; reduced gradients; projected-gradient methods; variational inequalities; box-constrained stochastic control.
  • Scientific computing: Implementation and testing of PDE and optimal-control algorithms; convergence studies; numerical simulation; visualization; reproducible computational experiments.

Selected publications and research works#

Preprints#

Accepted and published articles#

Grants#

  • Sep – Oct 2024: Travel grant from the 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 the University of Tübingen for visits to TIFR CAM Bangalore, IIT Delhi, IIT Roorkee, and IIT Ropar, India.
  • May 2023: Research grant from the 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 Integrated Ph.D. entrance examinations cleared: IIT Guwahati, IISER Bhopal, IISER Mohali, and TIFR CAM Bangalore.
  • 2013 – 2016: INSPIRE Scholarship for Higher Education, Department of Science and Technology, India.

Teaching experience#

Teaching and mentoring interests#

  • Core courses: Calculus, Linear Algebra, Ordinary and Partial Differential Equations, Probability, Real Analysis, Numerical Analysis, Functional Analysis, and Measure Theory.
  • Advanced courses: Numerical methods for differential equations, stochastic differential equations, numerical methods for SPDEs, stochastic optimal control, PDE-constrained optimization, Monte Carlo methods, and scientific computing.
  • Teaching approach: Clear mathematical foundations, structured problem solving, suitable Python-based exercises, and regular feedback. I am prepared to guide reading courses, summer projects, and research-oriented computational projects at undergraduate and postgraduate levels.

Teaching assistance#

  • April – July 2023: University of Tübingen, Prof. Andreas Prohl, Statistical Learning 2. Conducted tutorial classes (2 hours/week).
  • April – July 2023: University of Tübingen, Prof. Andreas Prohl, Statistical Learning 1. Conducted tutorial classes (2 hours/week).
  • November 2022 – February 2023: University of Tübingen, Prof. Andreas Prohl, Seminar Statistical Learning 1. Guided graduate students in preparing seminar talks (2 hours/week).
  • February 2020: TIFR-CAM, Prof. Martina Hofmanová, Stochastic Compressible Fluid Flows. Conducted discussion classes.
  • January – July 2020: TIFR-CAM, Prof. Ujjwal Koley, Fluid Mechanics. Conducted discussion classes and assigned grades.
  • August 2019: TIFR-CAM, NCMW – System of Conservation Laws Theory and Numerics, Hyperbolic Conservation Laws. Conducted discussion classes.
  • January – July 2019: TIFR-CAM, Prof. Ujjwal Koley, Measure Theory. Conducted discussion classes and assigned grades.
  • August – December 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#

  • August 2026: 2026 STOCHASTICA Colloquium, Niš, Serbia — A higher order discretization for the stochastic Navier–Stokes equations with additive noise.
  • June 2026: University of Duisburg–Essen, Germany — High-order time discretizations for SPDEs with additive noise.
  • May 2025: University of Bielefeld, Germany — An efficient, implementable discretization of stochastic linear–quadratic optimal-control problems and convergence with rates.
  • May 2025: ENS de Lyon, France — An efficient, implementable discretization of SLQ problem and convergence with rates.
  • April 2025: ICMS Edinburgh, United Kingdom — An efficient, implementable discretization of SLQ problem and convergence with rates.
  • September 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 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.
  • February 2024: TIFR CAM, Bangalore — An efficient discretization to simulate the solution of linear-quadratic stochastic boundary control problem.
  • February 2024: University of Tübingen — Stochastic linear quadratic optimal control problem.
  • May 2023: University of Pau, France — Measure-valued solution to incompressible Euler equations with stochastic forcing.

Conferences and workshops attended#

  • September 2025: Friedrich-Alexander University Erlangen–Nürnberg, Germany — Hyperbolic Problems in Nürnberg 2025.
  • July 2025: University of Nottingham, United Kingdom — Milstein’s Method: 50 Years On.
  • April 2025: ICMS, Edinburgh, United Kingdom — Numerical Modelling of Nonlinear Stochastic Systems.
  • February 2025: Swiss MAP Research Station, Les Diablerets, Switzerland — Swiss MAP Workshop: Stochastic Equations and Stochastic Dynamics.
  • September 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.
  • September – December 2020: IIT Kanpur, IISER Pune, IISER Kolkata, TIFR-CAM — Webinar on PDE and related areas.
  • February 2020: TIFR-CAM, Bangalore — Compact course on mathematical aspects of stochastic compressible fluid flows, by Prof. Martina Hofmanová.
  • January – February 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, Prof. Kaushik Ramachandran, TIFR-CAM, 2019.
  • Harmonic Analysis, Dr. Ramesh Manna, TIFR-CAM, 2018.
  • Microlocal Analysis, Prof. Venkateswaran P. Krishnan, TIFR-CAM, 2018.
  • Kinetic Theory for Scalar Conservation Laws, Prof. K. T. Joseph, TIFR-CAM, 2018.
  • $L^p$ Theory for Elliptic PDEs, 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 related to compressible fluid flow equations (certificate).
  • Reviewer, Nonlinear Differential Equations and Applications NoDEA. Reviewed a paper related to mathematical analysis and SPDEs (certificate).
  • Reviewer, Computational Methods in Applied Mathematics (CMAM). Reviewed a paper related to SPDEs and numerical analysis (review record).
  • Reviewer, Zeitschrift für angewandte Mathematik und Physik. Accepted an invitation to review a paper related to well-posedness theory for a system of SPDEs.
  • Reviewer, Journal of Scientific Computing.