Rather than going to the NOG

III Workshop I think it is more fun to give a talk for the *Capita
Selecta*-course for 2nd year students on “Monstrous Moonshine”. If

I manage to explain to them at least something, I think I am in good

shape for next year\’s Baby Geometry (first year) course. Besides,

afterwards I may decide to give some details of Borcherds\’ solution next year in my 3rd year

Geometry-course…(but this may just be a little bit

over-optimistic).

Anyway, this is what I plan to do in my

lecture : explain both sides of the McKay-observation

that

196 884 = 196 883 + 1

that is, I\’ll give

the action of the modular group on the upper-half plane and prove that

its fundamental domain is just C using the modular j-function (left hand

side) and sketch the importance of the Monster group and its

representation theory (right hand side). Then I\’ll mention Ogg\’s

observation that the only subgroups **Gamma(0,p)+** of **SL(2,Z)**

for which the fundamental domain has genus zero are the prime divisors

**p** of teh order of the Monster and I\’ll come to moonshine

conjecture of Conway and Norton (for those students who did hear my talk

on *Antwerp sprouts*, yes both Conway and Simon Norton (via his

SNORT-go) did appear there too…) and if time allows it, I\’ll sketch

the main idea of the proof. Fortunately, Richard Borcherds has written

some excellent expository papers I can use (see his papers-page and I also discovered a beautiful

moonshine-page by Helena Verrill which will make my job a lot

easier.

Btw. yesterday\’s Monster was taken from her other monster story…

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