Last week I had a cold and could not do much thinking. So I spent my time making TikZ pictures for an upcoming talk of mine. This talk is on my recent work with Akihiro Munemasa on constructing cospectral strongly regular graphs. I think that the pictures are nice for a blog post, so here […]
This is the announced post on my recent paper with Yuval Filmus on Boolean degree $ {1}$ functions on association schemes. The post will focus on what motivates the problem from various points of view. Before I start, a small remark. I am using latex2wp for the first time in this post. Thanks to Luca […]
Permutation Groups, Analysis of Boolean Functions, Finite Geometry, Coding Theory and Algebraic Graph Theory Important mathematical concepts get reinvented many times. In my recent work with Yuval Filmus we explored objects that are called (in random ordering) Boolean degree 1 functions, Cameron-Liebler line classes, equitable partitions, completely regular strength 0 codes with covering radius 1, […]
This is a small report on a failed project — obtaining semidefinite programming bounds on constant dimension network codes. But let us start with some context … A network code consists of a set of subspaces in [latex]\mathbb{F}_q^n[/latex]. It is a code, so we want to maximize the distance between subspaces (or increase the code’s […]
This year is László Lovász‘s 70th birthday and I went to his birthday conference, so a blog post about one of his famous results seems to be appropriate: the chromatic number of the Kneser graph. Let $ \Gamma$ be a graph with a vertex set $ V$ and an adjacency relation $ \sim$. A coloring […]
Today’s topic combines three of my favorite subjects: Erdős-Ko-Rado theorems (EKR theorems), finite buildings and spectral techniques. All of these topics deserve their own books (and have them, here some examples which I read: Erdos-Ko-Rado Theorems: Algebraic Approaches by Chris Godsil and Karen Meagher, Spectra of Graphs by Andries E. Brouwer and Willem H. Haemers, The Structure of Spherical […]