  In this paper, we give alternative proofs of Bott periodicity of $ K $-theory
and the bulk-edge correspondence of integer quantum Hall effect. Regarding Bott
periodicity, we connect its proof with configuration spaces and use Quot
schemes in algebraic geometry in our proof. Regarding the bulk-edge
correspondence, we formulate edge indices based on the consideration of
Graf--Porta and give a more elementary and self-contained proof.
