We present a computation of spectra of random walks on self-similar graphs.

Discussing recent work joint with M. Rudnev [2], I will discuss the modern approach to the sum-product problem in the reals. Our approach builds upon and simplifies the arguments of Shkredov and ...

A square in a matrix $\mathcal M =(a_{ij})$ is a 2X2 sub-matrix of $\mathcal M$ with entries $a_{ij}, a_{i+s,j}, ai,j+s, a_{i+s,j+s}$s for some $s\geq 1$. An Erickson matrix is a square binary matrix ...

The Liouville function $\lambda(n)$ takes the value +1 or -1 depending on whether $n$ has an even or an odd number of prime factors. The Liouville function is closely related to the characteristic ...