This has been nearly finished for a long time. I thought I should finally release it on Father’s day, in honor of my dad who has made several attempts to understand group theory despite an ocean and 8 time zones separating us.
I am always unsure of how to explain what I do to non-mathematicians. In order to understand my research someone first has to understand some group theory, in particular character theory of finite groups. Group theory is a part of abstract algebra that deals with symmetry. For that reason it shows up throughout mathematics as well as physics, chemistry, cryptography, etc. Today, I won’t explain group theory, but I’ll give you a pretty picture of it’s greatest achievement: The Classification of Finite Simple Groups.
A major goal of group theory has been to characterize what types of finite groups can exist. That is to say, what…
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