some fun stuff

I often find that these academic webpages serve as cookie-cutter enterprises devoted to being easy paper-finding resources. Which isn’t really a bad thing, per se, but they do come off as devoid of personality; the subject usually ends up seeming stoic or unapproachable. It’s why I usually like adding a some irrelevant information about myself. It’s quite fun.

about me

I like travelling quite a bit and I’ve lived in a bunch of different places in my life. My favorite among these places is probably Bangalore, which happens to be my hometown, followed shortly by Paris. I also spent a fantastic year and a half in Chennai. Sometimes I write about these things. I also write short stories, satirical articles, and ocassionally poetry, although I’ve only recently started uploading some of my work. You can find it here. It’s not a very good website, but I guess it suffices. Eventually I’d like to make something out of writing.

I watch a lot of sports, though the only sport I regularly practice is running (and hiking? if you can call it one). I support Manchester United for no good reason, and I also have a soft spot for Borussia Dortmund. I also watch Formula 1, where I support McLaren. I enjoy arguing about football and F1. If you ever want to pick a fight, let me know. I’d be happy to oblige.

This is the lost media wiki, one of my favorite websites. It’s devoted to finding and archiving ‘lost’ media – ie, media that was once available for public viewing but can no longer be found.

At some point I gave the mathematical olympiad. I did pretty okay.

some papers

My area of interest is cryptography and theoretical computer science. Here’s a list of some of my favorite papers.

• The Random Oracle Methodology, Revisited. Article.
• A Proof of Security of Yao’s Protocol for Two-Party Computation. Article.
• The Rise of Paillier: Homomorphic Secret Sharing and Public-Key Silent OT. Article.
• Extending Oblivious Transfers Efficiently. Article.
• Two Halves Make a Whole: Reducing Data Transfer in Garbled Circuits using Half Gates. Article.

some open problems

While I work in cryptography, I like pretty much all kinds of math, including but not limited to: complexity theory, algorithms, combinatorics (especially extremal), number theory and algebraic geometry. Here are some open problems you probably won’t solve.

• Zarankiewicz’s Problem. Article. What is the maximum number of edges of a bipartite graph that does not contain \(K_{t,t}\)?
• Union-Closed Sets Conjecture. Article. Consider a family \(\mathcal{F}\) of subsets of a set \(X\) such that \(A,B\in\mathcal{F}\) implies \(A\cup B\in\mathcal{F}\). Then is there an element \(x\in X\) such that \(d(x)\geq \|\mathcal{F}\|/2\)?
• Frankl’s Antichain Conjecture. Consider a convex family of subsets of \([n]\), where a family \(\mathcal{F}\) is convex if \(A\subset B\subset C\) and \(A\) and \(C\) in \(\mathcal{F}\) implies that \(B\in\mathcal{F}\). Then prove that there is an antichain \(\mathcal{G}\) such that \(\|\mathcal{G}\|/\|\mathcal{F}\|\geq \binom{n}{\lfloor n/2\rfloor}/2^n\).