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.

An drawing of the Hitchin fibration. This is similar in concept to my previous picture, but emphasizing different aspects. Some aspects of note:

• the moduli space $Bun_G$ appears in the hitchin moduli space
• $Bun_G$ lives inside the nilpotent cone, but is not the entire nilpotent cone
• $Bun_G$ is "close to" a torus, in the sense that nearby fibers of the Hitchin fibrtion are tori
• The Whittaker sheaf is supported on the Hitchin section, This does not intersect $Bun(G)$ itself, rather another irriducible component ot
• The Whittaker sheaf plays the role of the color white in the spectral decomposition of geometric Langlands. Hence i drew it as a white field of wheat. The name Whittaker translates to "white field"

A picture of the moduli space of $G$-bundles, emphasizing its stratification. Each layer has boundary consisting of the layer above.