PhD researcher in Applied Mathematics at Dr. Krešo's lab, University of Houston
I work at the intersection of computational neuroscience, dynamical systems, and neural data analysis, with an interest in how mathematical structure can help explain neural computation and representation.
Questions I am interested in
My research interests connect mathematical modelling with neural computation, population-level representations, and data-driven analysis.
Neural Representation
Understanding the geometry and structure of population activity, including how neural systems represent task variables and abstract quantities.
Neural Circuit Modelling
Studying mathematical models of neurons and circuits using nonlinear dynamics, stability, bifurcation theory, and computational simulation.
Neural Data Analysis
Using statistical and computational tools to analyze spike trains, neural population activity, and low-dimensional structure in high-dimensional data.
A little about me
Officially I’m Abdul Rahman, also known as Shafiq, and I often go by A.B. (/eɪ biː/) — pick your favorite.
I am a PhD researcher in Applied Mathematics at the University of Houston. My mathematical background spans dynamical systems, probability, stochastic analysis, mathematical biology, statistics, and mathematical finance. I am especially interested in using mathematics and computation to understand complex biological systems, particularly the brain.
Before beginning my PhD, I completed an M.Sc. in Mathematics at IIT Madras. My earlier research interests included limit-order-book modelling, stochastic processes, machine learning, agent-based simulation, reinforcement learning, and time-series methods in financial markets.
Outside academics, I enjoy painting, photography, soccer, chess, fitness, and thought-provoking films. I am always happy to connect with people interested in mathematics, neuroscience, computation, or interdisciplinary research.
Academic journey
- Master’s thesis: Technical Analysis in Mathematical Finance
- Institute Merit Scholarship recipient
- Coursework included stochastic calculus in finance, stochastic processes, probability and measure theory, mathematical finance, applied statistics, differential equations, functional analysis, and data visualization.
- Undergraduate project: Linear Algebra and its Applications in Machine Learning
- Minor coursework in Physics and Statistics
- First Rank Holder · Gold Medalist
Professional highlights
Expanded academic history is kept here so the homepage stays focused on current research while still preserving the details.
Professional Memberships
- Organization for Computational Neurosciences (OCNS), Student Member
- Society for Industrial and Applied Mathematics (SIAM), Student Member / UH Student Chapter
Honors & Awards
- 2026: NSM Alumni Association (Eckhard Pfeifer/Carolyn Farb) Scholarship, University of Houston Alumni Association Foundation (UHAAF), 2026–2027 Academic Year
- 2025: Qualified CSIR NET, JRF — Eligible to be Assistant Professor in India
- 2024: Qualified Graduate Aptitude Test in Engineering (GATE)
- 2022: All India Rank 196 in IIT-JAM (among 12,716 mathematics aspirants)
- 2021: Rank 1, Department of Mathematics, Government Arts College, Coimbatore
- 2018: District Runner, Mathematics Model Exam, CSI College of Engineering, Nilgiris, India
- 2018: Rank 1, Young Ramanujam of School Award, Dhanish Ahmed Institute of Engineering, Coimbatore
- 2016: Nilgiri District Achiever, Tamil Nadu School Associations
- 2016: Kaitlyn Jeyaraj & Bryan Wood Cash Award for Centum in Mathematics
Seminars & Presentations
- June 2024: Contributory lectures on “Gaussian Functions, Errors and Stirling’s Approximations” — Summer Workshop on Pure Mathematics
- April 2024: Presented “Itô's Rule” proof under Prof. Neelesh Upadhye, IIT Madras — Mathematical Finance
- Feb 2024: Presented approximation of a class of functions by simple functions using convolution and measure theory under Prof. Barun Sarkar, IIT Madras
- Feb 2024: Seminar on “Itô's Integration” for research scholars under Prof. Barun Sarkar, IIT Madras
- May 2023: Seminar on “GCD over Euclidean Domains” — Mathematics Training and Talent Search Programme, IIT Madras
- May 2022: Co-led discussion on “Significance of Eigenvalues and Eigenvectors” with Dr. Saranya, Government Arts College, Coimbatore
Workshops & Conferences
- 2026: Summer School on Stochastic Dynamics and Persistence in Biology, Texas A&M (Jun 21–27)
- 2024: Mini Course on Markov Chains by Prof. Manjunath Krishnapur, IISc Bangalore
- 2024: International FDP on Financial Mathematics, SPDE Theory, and Mathematical Modeling — VIT AP University
- 2024: International Conference on Stochastic Calculus & Applications to Finance — King’s College London & IIT Madras
- 2024: Workshop on Valuation of Equity Options using the Black–Scholes Model — IIQF
- 2024: Python in Finance & Open Range Breakout Strategy Workshop — StockGro at IIT Madras
- 2024: Statistical Modeling & Quant Challenge — Millennium Investment Management, IIT Madras
- 2024: Advanced Training School on PDEs & MATLAB — K. J. Somaiya College, Mumbai
- 2023: One-month Summer School integrating Linear Algebra, Probability, Markov Chains, and Differential Equations — IIT Madras
- 2023: MTTS Programme — Linear Algebra, Complex Analysis, Topology, Module & Ring Theory, IIT Madras
- 2023: Mathematics In-house Symposium — IIT Madras
- 2022: National Conference on Computational Mathematics — NIT Puducherry
- 2022: Workshop on Nonlinear Phenomena in Mathematical Biology — IIITM Gwalior
- 2021: NPTEL Modern Algebra Course — Madurai Kamaraj University
- 2021: KLA Workshop on AI & HPC in Semiconductor Manufacturing — IIT Madras
- 2020: Initiation into Linear Algebra — International Workshop, Mar Thoma College
- 2020: Vedic Mathematics & Foundations — Government Arts College, Coimbatore
Entrepreneurial & Extracurricular Activities
- Professional Coaching — Theory & Thought: Guided thinking and mentorship in Mathematics and Statistics for graduate learners (Jun 2025–Present)
- Organizer & Initiator: Weekly Student Seminar Series, Department of Mathematics, IIT Madras (Nov 2023–May 2024)
- Student Chief Coordinator: MTTS Programme, IIT Madras (May 2023) — Facilitated 150+ students
- Super Coordinator: FORAYS 23, IIT Madras (Feb 2023) — Annual mathematics fest
- Founder: SMART CART OFFICIAL — Online art & craft studio (Jan 2019–Jun 2025)
- Photographer: EYES OF ABDUL — Photography & videography portfolio