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the monster dictates her picture

The monstrous moonshine picture is a sub-graph of Conway’s Big Picture on 218 vertices. These vertices are the classes of lattices needed in the construction of the 171 moonshine groups. That is, moonshine gives us the shape of the picture. (image credit Friendly Monsters) But we can ask to reverse this process. Is the shape […]
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Moonshine’s green anaconda

Academics / Mathematics : Neverendingbooks

The largest snake in the moonshine picture determines the moonshine group $(24|12)$ and is associated to conjugacy class $24J$ of the monster. It contains $70$ lattices, about one third of the total number of lattices in the moonshi...

the monstrous moonshine picture – 1

Academics / Mathematics : Neverendingbooks

We’re slowly closing in on the elusive moonshine picture, which is the subgraph of Conway’s Big Picture needed to describe all 171 moonshine groups. About nine years ago I had a first go at it, drawing a tiny fraction of it, just en...

the monstrous moonshine picture – 2

Academics / Mathematics : Neverendingbooks

Time to wrap up my calculations on the moonshine picture, which is the subgraph of Conway’s Big Picture needed to describe all 171 moonshine groups. No doubt I’ve made mistakes. All corrections are welcome. The starting point is the...

A forgotten type and roots of unity (again)

Academics / Mathematics : Neverendingbooks

The monstrous moonshine picture is the finite piece of Conway’s Big Picture needed to understand the 171 moonshine groups associated to conjugacy classes of the monster. Last time I claimed that there were exactly 7 types of local b...

the moonshine picture – at last

Academics / Mathematics : Neverendingbooks

The monstrous moonshine picture is the subgraph of Conway’s big picture consisting of all lattices needed to describe the 171 moonshine groups. It consists of: – exactly 218 vertices (that is, lattices), out of which – 97 are number...

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