Video Lectures

A fake projective plane is a smooth complex projective algebraic surface whose Betti numbers are same as those of the complex projective plane but which is not the complex projective plane. The first fake projective plane was constructed by David...

We study particular solutions of the "inner equation" associated to the splitting of separatrices on "generalized standard maps". An exponentially small complete expression for their difference is obtained. We also provide numerical evidence that...

Zaremba's 1971 conjecture predicts that every integer appears as the denominator of a finite continued fraction whose partial quotients are bounded by an absolute constant. We confirm this conjecture for a set of density one.

In this talk I will present a colored version of Tverberg's theorem about partitioning finite point sets in R^d into rainbow groups whose convex hulls intersect. This settles the famous Bárány-Larman conjecture (1992) for primes minus one, and...

We study the setting in which the bits of an unknown infinite binary sequence x are revealed sequentially to an observer. We show that very limited assumptions about x allow one to make successful predictions about unseen bits of x . Our main focus...

I will discuss a middle-dimensional generalization of Gromov's Non-Squeezing Theorem.

I will discuss a middle-dimensional generalization of Gromov's Non-Squeezing Theorem.

We review some recent developments in KAM theory. By exploiting some identities of a geometric nature, one can obtain iterative steps which lead to numerical algorithms and which can follow the tori till breakdown. We present theoretical results in...

A randomness extractor is an efficient algorithm which extracts high-quality randomness from a low-quality random source. Randomness extractors have important applications in a wide variety of areas, including pseudorandomness, cryptography...