# Mathematics

### Ramanujan complexes and golden gates in PU(3).

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....

### Distribution of the integral points on quadrics

Motivated by questions in computer science, we consider the problem of approximating local points (real or p-adic points) on the unit sphere S^d optimally by the projection of the integral points lying on R*S^d, where R^2 is an integer. We present...

### Time quasi-periodic gravity water waves in finite depth

Massimiliano Berti
We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water waves solutions, namely periodic and even in the space variable $x$, of a bi-dimensional ocean with finite depth under the...

### 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...

### Morse-Bott cohomology from homological perturbation

Abstract: In this talk, I will give a new construction of the Morse-Bott cochain complex, where the underlying vector space is generated by the cohomology of the critical manifolds. This new construction has two nice features: (1) It requires the...

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

Barna Saha

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?

Sanjeev Arora and Richard Zemel
https://www.ias.edu/events/arora-zemel-publiclecture

### Continuous covers on symplectic manifolds

François Lalonde

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...

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

Alexander Wright

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...

### General Relativity at 100

https://www.ias.edu/gr100 Albert Einstein’s general theory of relativity, a pillar of modern physics formulated 100 years ago, will be celebrated by the Institute for Advanced Study and Princeton University in a two-day conference, General...