Langlands drawings
Summary:
Drawings of some objects from the Geometric Langlands correspondence. These figures were drawn on commission for David Ben-Zvi
Gallery
The Mellin transform on Sheaves
On the left, we have a picture of $Loc(\CC^\ast)$. This consists of local systems, drawn as covering spaces over the gravley $\mathbb{C}^\ast$. On the right, we have the spectral side $Qcoh(\CC^\ast)$. The Mellin transform on sheaves is an equivalence of categories between $Log(\CC^\ast)$ and $Qcoh(\CC^\ast)$. I drew this as a literal “spectral decomposition”, a splitting of each local system into its component specters. The local systems corresponding to covering maps get mapped by specters to single points. The skyscraper sheaf plays the role of white light, as it decomposes to one of each spectrum.