Research and Publications

Research Experiences & Interests:

My research interests have always been driven by following interesting problems that combine deep mathematical theory with real-world applications. My current research interests include:

📊 Machine Learning/Deep Learning/Statistics:

• Causal Inference and Machine Learning,
• LLMs (Multi-Agent Systems, Mechanistic Interpretability, and Applications),
• Mathematical/High-dimensional Statistics, and
• Time-Series Models and Analysis.

Differential Topology:

• Genericity, Transversality, and Applications (to math/data science/machine learning).

These have evolved from earlier work as a graduate and an undergraduate student, where I have worked on projects involving:

• Hyperbolic PDEs and Conservation Laws: Analysis & Applications.
• Mathematical general relativity,
• Bayesian modeling in nuclear astrophysics, and
• Numerical methods in quantum field theory.

Throughout, I think of myself as a “full stack mathematician” — I take projects end-to-end, from theory and modeling through implementation and simulation to production-scale systems whenever possible!

In Progress:

📋 Causal Lag Structure Discovery in Confounded Time Series via Orthogonalized Adaptive Estimation
       (submitted for a conference)
       Tags: Causal Machine Learning, Time Series Analysis.
       📊 GitHub Repo.

📋 Macroscopic Traffic Flow Network Simulations for Wildfire Evacuation
       Tags: Optimization, PDEs on Graphs, Numerical Analysis, Mathematical Modelling.
       🚦 GitHub Repo.

📋 Automated Circuit Discovery for Real-time Internal Monitoring
       Working on it as a Research Fellow under SPAR with Sriram Balasubramanian.
       Tags: LLMs, AI Alignment, Causal Inference, Mechanistic Interpretability.

📋 Generic Structural Stability for n x n Systems of Hyperbolic Conservation Laws
       Tags: Analysis of PDEs, Differential Topology, Functional Analysis, Numerical Analysis.

Publications:

📜 Beyond Statistical Changepoint Detection: Semantic Interpretation of Time Series via LLMs
       Work done as an intern at Amazon,
       with Trilokya Akula, Akash Tonne, Thomas Blake.
       Accepted at ICLR 2026 Time Series in the Age of Large Models Workshop (Poster).
       Tags: Mathematical Statistics, LLMs, Multi-agent Systems.

📜 Generic Structural Stability for 2 x 2 Systems of Hyperbolic Conservation Laws
       with Andrea Bertozzi.
       arXiv:2502.08998 (2025),.
       Accepted to SIAM Journal of Mathematical Analysis.
       Tags: Analysis of PDEs, Differential Topology, Functional Analysis, Numerical Analysis, Fluid Dynamics.
       📋 Slides.

📜 Weak Cosmic Censorship Conjecture for the Spherically Symmetric Einstein-Maxwell-Charged Scalar Field System
       with Xinliang An.
       arXiv:2402.16250 (2024).
       Tags: Analysis of PDEs, General Relativity.

📜 Regularization of Complex Langevin Method
       with Zhenning Cai and Yang Kuang.
       Phys. Rev. D 105, 014508 (2022).
       Tags: Numerical Analysis, Statistics, Quantum Mechanics.

📜 Hierarchical Bayesian Thermonuclear Rate for 7Be(n,p)7Li Big Bang Nucleosynthesis Reactions
       with Rafael S de Souza, Alain Coc, and Christian Iliadis.
       The Astrophysical Journal 894, 132 (2020).
       Tags: Bayesian Statistics, Astrophysics.

You can access my Google Scholar here.