My dissertation, PDEs and Machine Learning with Applications in Medical Imaging, develops optimization methods with provable guarantees and applies them to inverse problems and imaging. Current work learns proximal operators with input-convex neural networks and connects them to Hamilton–Jacobi equations, giving a route to reconstruction that avoids solving an optimization problem at every query. An ongoing project carries these ideas into medical image registration, where aligning two scans amounts to a large-scale, ill-posed optimization problem over deformation fields. Earlier work analysed momentum-based minimization of the Ginzburg–Landau functional on Euclidean spaces and graphs.

• Onboarded 40 master's students to the required class tools (Jupyter Notebooks, Google Colab, Slack, Git, and LaTeX) and provided technical troubleshooting and debugging support.
• Led two hours of weekly practice sessions plus an additional office hour.
• Prepared six major homework projects, implementing LaTeX/Overleaf protocols and standardizing version control for student submissions.
• Facilitated office hours and Slack discussions, resolving questions on optimization theory and debugging code in Google Colab.
• Graded assignments covering linear algebra, deterministic and stochastic optimization, and statistics, meeting compressed summer session deadlines.

• Instructed undergraduate students across three mathematics courses.
• Prepared lecture notes and graded all coursework, exams, and assessments.
• Mentored students needing additional support to bridge gaps in technical skills.
• Supervised two final-year student dissertations.