Goal.
I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much.
This time.
What are...sporadic groups? Or: Weird, but interesting.
Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.
Slides.
www.dtubbenhauer.com/youtube.html
TeX files for the presentation.
github.com/dtubbenhauer/My-Te...
Thumbnail.
en.wikipedia.org/wiki/Hall%E2...
Main discussion.
en.wikipedia.org/wiki/Sporadi...
www.ams.org/journals/notices/...
en.wikipedia.org/wiki/Classif...
en.wikipedia.org/wiki/List_of...
en.wikipedia.org/wiki/Group_o...
plus.maths.org/content/enormo...
Background material.
en.wikipedia.org/wiki/Group_(...)
en.wikipedia.org/wiki/Simple_...
en.wikipedia.org/wiki/Normal_...
en.wikipedia.org/wiki/Finite_...
en.wikipedia.org/wiki/Composi...
en.wikipedia.org/wiki/Categor...
en.wikipedia.org/wiki/Mathieu...
en.wikipedia.org/wiki/Janko_g...
en.wikipedia.org/wiki/ATLAS_o...
Computer talk.
Run the below Magma code here: magma.maths.usyd.edu.au/calc/
G:=Group("M11");
CharacterTable(G)
M11 can be replaced by any other (not too large) sporadic group using the Atlas notation en.wikipedia.org/wiki/ATLAS_o....
Pictures used.
Picture from • What is...the discrete...
A zoom in and modification of the same picture
en.wikipedia.org/wiki/Klein_q...
Another zoom in and modification of the same picture
Picture from en.wikipedia.org/wiki/Janko_g...
en.wikipedia.org/wiki/Fano_pl...
More Fano planes
en.wikipedia.org/wiki/Hall%E2...
KZitem and co.
• Sporadic groups
• Why Do Sporadic Groups...
• Math talk: Sporadic gr...
• Sporadic Groups - Prof...
#grouptheory
#combinatorics
#mathematics
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