I'm currently traversing the vast, uncharted universe that is complexity theory. It's like weaving through a starry cosmos, where each problem shines like a distant star, and solutions form intricate constellations. Just as the vastness of space conceals unseen forces that bind galaxies, the realm of complexity theory unveils hidden structures that shape our understanding of what can be solved and what lies beyond reach. It's a journey through an endless universe, where the pursuit of discovery is the ultimate reward.

Intellectual Curiosity

I'm endlessly fascinated by the big questions in theoretical computer science, the elegance of mathematics, and the craft of programming languages.

In theoretical computer science, abstract ideas have real-world consequences. One question that keeps me up at night is the P vs NP problem: Can every problem that can be quickly verified also be quickly solved? A definitive answer would not only deepen our understanding of computation—it could alter our very perception of reality itself. Broadly speaking, complexity theory dives deep into these kinds of questions. This exploration is profound and has far-reaching applications, impacting everything from cryptography to artificial intelligence. Yet, theoretical computer science is more than just complexity theory. It encompasses a wide variety of topics like algorithms, quantum computation, automata theory, information theory, cryptography, program verification, and more.

Mathematics, with its depth and elegance, offers an intellectual adventure that continually challenges and inspires. Gödel's incompleteness theorem reveals a profound paradox at the heart of formal logic: there are true mathematical statements that can never be proven. This result not only challenges our undersanding of formal axiomatic theories but also forces us to confront the very nature of knowledge and certainty itself. Monstrous moonshine, an astonishing result connecting algebra, complex analysis, number theory, and even string theory. This unexpected link reveals how seemingly unrelated areas of mathematics and physics are intertwined in ways that defy intuition, as though we're uncovering a hidden thread woven into the very fabric of the universe. Such discoveries underscore the beauty and surprise of mathematics: abstract, seemingly disconnected ideas converging in ways that feel both inevitable and magical.

Programming languages sit at a unique intersection of theory and practice. Exploring their design uncovers a captivating interplay between the fundamental principles of computation and the practical demands of software engineering. How does a compiler transform high-level code into machine-executable instructions? Why are some languages more prone to bugs or security vulnerabilities than others? And why do certain languages shine in specific domains, like web development or system programming? These are just a few of the questions that make programming languages a continually evolving field, where deep theoretical foundations meet the tangible challenges of building real-world systems. It's a domain where the pursuit of knowledge is as intellectually stimulating as it is practically essential.

Research Interests

I'm drawn to research that bridges theory and practice, particularly at the intersection of programming languages and security—exploring formal methods, logic, and their application to both programming languages and computer systems. Currently, I'm very fortunate to be working with the amazing Prof. Umang Mathur, tackling exciting challenges like automated program verification and developing novel algorithmic techniques to detect and analyze bugs in programs. The ultimate goal is to develop tools and methods that enhance software security, reliability, and clarity—making code not only safer but also more intuitive and enjoyable to work with.

Life Beyond Academia

I find inspiration in storytelling and music. I'm a big fan of transformative media—whether it's anime that explores mind-bending concepts or films that push the boundaries of narrative and art. My music diet consists mostly of classical, with occasional forays into Japanese pop and rock. When the moment calls for it, you'll likely find me playing the classical guitar, channeling my inner musician and letting the harmony take me somewhere else. If you're looking for anime recommendations or want to chat about the classical guitar, feel free to hit me up!

For the curious, my current "song" on repeat is Rondo No. 2 Op. 2 by Dionisio Aguado.