CV

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Research Interests

Numerical analysis and scientific computing for deterministic and stochastic partial differential equations, including finite element methods, PDE-constrained optimization, adjoint-based solvers, CVaR regularization, and operator-theoretic foundations, with applications to mathematical physics and related applied problems.

Education

• Ph.D. in Mathematics, George Mason University, Fairfax, Virginia, USA
  • Jan 2025 – Present
  • Advisor: Dr. Harbir Antil
• M.Sc. in Mathematics, Indian Institute of Technology Roorkee, India
  • July 2022 – May 2024
  • CGPA: 8.66/10
  • Supervisor: Prof. Ankik Kumar Giri
  • Thesis: Deterministic and Stochastic Conservation Laws
• B.Sc. (Honours) in Physics, Ramjas College, University of Delhi, India
  • July 2019 – May 2022
  • CGPA: 7.9/10

Skills

• Programming: Python, C++, MATLAB
• Scientific Computing: Numerical methods for PDEs, finite element methods, numerical linear algebra
• Tools: LaTeX, Linux-based workflow, Git & GitHub

Publications

Conditional Value-at-Risk Regularization of Exceedance Functionals: Analysis, Duality, and Numerical Approximation

Antil, H., Bustos, B., and Jain, A. (2026). "Conditional Value-at-Risk Regularization of Exceedance Functionals: Analysis, Duality, and Numerical Approximation." In preparation.

Fisher-Information-Based Sensor Placement for Structural Digital Twins: Analytic Results and Benchmarks

Jain, A., Antil, H., and Löhner, R. (2026). "Fisher-Information-Based Sensor Placement for Structural Digital Twins: Analytic Results and Benchmarks." arXiv:2602.02981.

Teaching

• Graduate Teaching Assistant — Ordinary Differential Equations, George Mason University, Fall 2025
  Led weekly recitation sessions, held office hours, and assisted with grading.

• Seminar Leader — PDE Control Seminar, George Mason University, Fall 2025
  Delivered seminar lectures on PDE theory through well-posedness of elliptic equations and topics in nonlinear analysis relevant to PDE-constrained problems.

Awards and Honors

• IIT–JAM (Mathematics), All India Rank 191, March 2022
  National-level graduate entrance examination; acceptance rate ~6%.
• Academic Excellence Award, Ryan International School, July 2019
  Gold Medal for Rank 1 in Science Stream (Board Examinations); 7th in the District.

Conferences and Workshops

• Finite Element Circus, George Mason University, Arlington Campus, October 17–18, 2025
  Attended invited talks on finite element methods and numerical analysis of PDEs.

Selected Coursework

Functional Analysis I–II, Nonlinear Functional Analysis, Numerical Analysis, Theory of Partial Differential Equations, Measure Theory, Operator Theory, Financial Mathematics, Advanced Complex Analysis, Topology.