# Computer Science and Discrete Mathematics (CSDM)

## Rigidity of random Toeplitz matrices with an application to depth three circuits

## Lower bounds on the size of semidefinite programming relaxations

## General systems of linear forms: equidistribution and true complexity

## Advances on Ramsey numbers

## Cohomology for computer science II

We will start with presenting the basic notions of (co)homomology of simplical complexes (which requires only basic linear algebra over the field of order 2) and then we will indicate its relevance for several topics in computer science and combinatorics: 1) Property testing. 2) Quantum error correcting codes (where triangulation of some 4-dim hyperbolic manifolds lead to such codes with unexpected parameters) 3) High dimensional expanders. 4) Random simplical complexes.

## Cohomology for computer science

## How quaternion algebras over number fields are useful for creating compiler for a quantum computer?

## Cutting plane method: A faster algorithm for many (combinatorial) optimization problems

## Two-source dispersers for polylogarithmic entropy and improved Ramsey graphs II

In his 1947 paper that inaugurated the probabilistic method, Erdős proved the existence of $2 \log(n)$-Ramsey graphs on $n$ vertices. Matching Erdős' result with a constructive proof is a central problem in combinatorics that has gained a significant attention in the literature. In this talk we will present a recent work towards this goal (http://eccc.hpi-web.de/report/2015/095/).