# Computer Science and Discrete Mathematics (CSDM)

## Asymptotic spectra and their applications II

Matrix rank is well-known to be multiplicative under the Kronecker product, additive under the direct sum, normalized on identity matrices and non-increasing under multiplying from the left and from the right by any matrices. In fact, matrix rank is the only real matrix parameter with these four properties.

## Breaking the Circuit-Size Barrier in Secret Sharing

Based on joint work with Tianren Liu and Hoeteck Wee.

## Asymptotic spectra and their applications I

Matrix rank is well-known to be multiplicative under the Kronecker product, additive under the direct sum, normalized on identity matrices and non-increasing under multiplying from the left and from the right by any matrices. In fact, matrix rank is the only real matrix parameter with these four properties.

## Tensor rank

## Oracle Separation of Quantum Polynomial time and the Polynomial Hierarchy

## Four and a half proofs of a product-measure version of the Erdös-Ko-Rado Theorem.

The EKR theorem, which is the cornerstone of extremal combinatorics, characterizes maximal intersecting families of sets. Its setting fixes a ground set of size n, and then studies the size and structure of intersecting families of subsets of fixed size k. A setting which many might consider no less natural, is considering the Boolean lattice of all subsets of {1,...,n} endowed with a product measure, and studying the structure and measure of maximal intersecting families.

## A simple proof of a reverse Minkowski inequality

We consider the following question: how many points with bounded norm can a "non-degenerate" lattice have. Here, by a "non-degenerate" lattice, we mean an n-dimensional lattice with no surprisingly dense lower-dimensional sublattices.