Research Focus
My research sits at the intersection of Number Theory, Chaos Theory, and ALU architecture, seeking efficiency gains beyond conventional asymptotic analysis. The goal is to develop novel algorithms that exploit the underlying structure of computations to maximize performance at the hardware level.
Theoretical Foundations
- Optimizing computationally expensive operations (e.g., exponentiation) through Binomial Convolutions.
- Utilizing Dyadic Maps and Chaotic Mappings for efficient, deterministic sequence generation and encoding.
- Investigating complexity and hardness bounds in the context of spectral and lattice-based cryptography.
Applied Systems & Architecture
- Designing algorithms that leverage Memoized Encoding and highly efficient ALU Operations for minimal CPU time.
- Applying principles from scalable cloud architecture (AWS) to theoretical models for guaranteed resilience and performance.
- Experience in C/C++ and Haskell for low-level, high-performance implementations.
Projects & Liturature
Representing Exponents as Linear Combinations Write Up
Focus: Novel method for exponential evaluation by transforming exponents into simpler ALU operations using successive midpoints, binomial convolutions, and inverse dyadic mapping. (Related to Kyber/Dilithium algebraic foundations).
Probabilistic Data Structures: Bloom Filters Write Up
Focus: Discussing implementations, complexitiy, and usages of probabolistc Bloom Filters.
Enterprise Cloud Migration & Resilient Architecture
Focus: Leading the migration of core legacy services (mail, file, web) to the AWS public cloud, architecting solutions for low RTO/RPO, cost optimization, and high availability against hardware failure and natural disaster.
Undergraduate Project: Web Game
Focus: Creating a webgame with custom frontend rendering, random terrain generation, and cgi bin api calls
Graduate Project: Greedy 3D Bin Packing Visualization
Focus: Implemented a greedy algorithm for optimal visualization of complex warehouse purchase orders, ensuring maximal packing density using JavaScript and 3JS.
Graduate Database Project: Web Resourse Monitoring
Focus: Creating a logging system that tracks user sessions on both the front and back ends
Technical & Theoretical Aptitude
Languages
C, C++, Haskell, Java, JavaScript, Matlab, PHP, Python, Shell, SQL
Cloud & Infrastructure
AWS (SAA C03), Azure, Linux, SSH, Git, WHM
Applied Theory
Number Theory, Algorithmic Complexity, Fourier Analysis, Lattice Cryptography
Web/Tools
Tailwind, Bootstrap, 3JS, MongoDB, Matlab, Adobe Suite