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#

A. Chaudhary, Higher order numerical schemes for SPDEs with additive noise, preprint 2025.
A. Chaudhary, A numerical method to simulate the stochastic linear-quadratic optimal control problem with control constraint in higher dimensions, preprint 2024.
A. Chaudhary, U. Koley, E. Wiedemann, Dissipative measure-valued solutions to Euler-alignment system, preprint 2024.
A. Chaudhary, F. Merle, A. Prohl, Y. Wang, An efficient discretization to simulate the solution of linear-quadratic stochastic boundary control problem, IMA J. Numer. Anal. (2025) 00, 1–55.
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 U. 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 U. Tübingen, for a visit to TIFR CAM Bangalore, IIT Delhi, IIT Roorkee, IIT Ropar, India.
May 2023: Research grant from U. 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 U. 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 2025 – present: Teaching, U. Tübingen (Financial Mathematics and Numerics, 3h/week)
Oct 2024 – Feb 2025: Teaching, U. Tübingen (Numerical Optimization, 3h/week)
April – July 2024: Teaching, U. Tübingen (Optimal control theory with ODE and numerics, 3h/week)
Oct 2023 – Feb 2024: Teaching, U. Tübingen (Stochastic differential equations with numerics, 3h/week)
April 2024 – July 2024: Co-instructor, U. Tübingen (instructor: Prof. Andreas Prohl, Statistical Learning 1). Conducted discussions with graduate students to prepare seminar talks (2h/week).

Teaching assistance#

April 2023 – July 2023: U. Tübingen (Prof. Andreas Prohl, Statistical Learning 2). Conducted tutorial classes (2h/week).
April 2023 – July 2023: U. Tübingen (Prof. Andreas Prohl, Seminar Statistical Learning 1). Conducted tutorial classes (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.