# Mathematics

## Pseudorandom generators for unordered branching programs

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 Zuckerman where they required seed length $n^{1/2+o(1)}$.

## Morse-Bott cohomology from homological perturbation

## Language edit distance, $(\min,+)$-matrix multiplication & beyond

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 substitutions required to convert a given input string into a valid member of the language. In 1972, Aho and Peterson gave a dynamic programming algorithm that solves this problem in time cubic in the string length. Despite its vast number of applications, in forty years there has been no improvement over this running time.

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

## Continuous covers on symplectic manifolds

## Billiards in quadrilaterals, Hurwitz spaces, and real multiplication of Hecke type

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 Alex Eskin, Curtis McMullen, and Ronen Mukamel.