In their seminal works from the 80's, Lubotzky, Phillips and Sarnak proved the following two results: (i) An explicit construction of Ramanujan regular graphs. (ii) An explicit method of placing points on the sphere uniformly equidistributed....

#
Mathematics

We present an explicit pseudorandom generator with seed length $\tilde{O}((\log n)^{w+1})$ for read-once, oblivious, width $w$ branching programs that can read their input bits in any order. This improves upon the work of Impaggliazzo, Meka and...

The language edit distance is a significant generalization of two basic problems in computer science: parsing and string edit distance computation. Given any context free grammar, it computes the minimum number of insertions, deletions and...

### Public Lecture: Machines: How Do They Learn and Where Are They Headed?

In this talk, we first introduce the notion of a *continuous
cover* of a manifold parametrised by any compact manifold
endowed with a mass 1 volume-form. We prove that any such cover
admits a partition of unity where the usual sum is replaced
by...

After a brief introduction to the dynamics of the $\mathrm{GL}(2,\mathbb R)$ action on the Hodge bundle (the space of translations surfaces), we will give a construction of six new orbit closures and explain why they are interesting. Joint work with...