My previous post discussed one of the mayor open problems in spectral graph theory: the conjecture by van Dam and Haemers which asks to show that almost all graphs are determined by their spectrum. Unfortunately, the proof techniques required to address this conjecture appear to be lacking at the moment. Even numerical investigations are difficult…

# Blog

## Can one hear the shape of a graph? – Part 1

The eigenvalues $\lambda_1 \geq \cdots \geq \lambda_n$ of the adjacency matrix of a graph encode a lot of information. For instance, an elegant bound on the chromatic number is known due to Hoffman. There are so many structural properties which admit good spectral estimates that one may start to wonder whether the spectrum perhaps contains…

## HTML support on arXiv could be great!

I am excited about a recent accessibility update which added a HTML format to arXiv! Here are a few potential applications which are enabled by HTML being a more flexible format than PDF: At the moment, the HTML format still suffers from some bugs because converting LaTeX to HTML is nontrivial. (Under the hood, this…

## Ising model in my apartment

For a long time, the walls in my apartment have been empty. So empty that looking at them was like staring into the void and having the void stare right back at you. My girlfriend and I recently solved this situation by making a custom piece of art! Concretely, we painted a picture of the…

## What is the trace?

Any student of mathematics learns that the determinant of a matrix can be interpreted as the amount that the matrix distorts signed volume. The trace is another linear algebraic invariant but its interpretations are not common knowledge. This is somewhat troubling since the trace, being such a basic invariant, occurs in many proofs across mathematics….