Ferdinand Ihringer（Ghent University）「Three Perspectives on Boolean Degree $1$ Functions」
We discuss the equivalence of Cameron-Liebler line classes in finite geometry, completely regular strength $0$ codes with covering radius $1$ in algebraic combinatorics, and Boolean degree $1$ functions in the analysis of Boolean functions. All three disciplines have different perspectives on Boolean degree $1$ functions — they ask and solve (slightly) different questions about them. After discussing the general picture, we focus on Boolean degree $1$ functions in geometrical settings, mostly vector spaces, and recent classification results by Gavrilyuk and Matkin as well as Yuval Filmus and the speaker.