From hyperelliptic to superelliptic curves
Coverings
Function Fields
Curves
Automorphisms
Hurwitz Spaces
Moduli spaces of curves
Describing points in the moduli
Weighted moduli spaces
Equations of curves
Theta functions
Jacobian varieties
Complex multiplication
Obstruction in the moduli
Reduction theory of binary forms
Theory of heights
Minimal models
Mordell-Weil group for superelliptic Jacobians
Words of wisdom
"I can't believe they destroyed a perfectly good old farm to build this damn university" (From an old colleague)
“… Maybe you’ll find yourself in a mediocre department, where your work will be intentionally undervalued, people with much lesser research record will be promoted before you, and the hypocrites and frauds will run wild. Don’t get discouraged, don’t give up! Remember why you got into math?! It wasn’t for the money, recognition, or fame, it was for that special feeling that you get when you find the perfect solution or understand a beautiful argument. That hasn’t changed, son! If you still got that magical feeling, then you are doing fine.” (From Dad)
David Hilbert’s radio address - English translation.
“… There is a secret to mathematics. Do what you can, not what you dreamed of doing! And try to learn from any paper that you write.” (John Thompson after my dissertation defense)
“Certainly the best times were when I was alone with mathematics, free of ambition and pretense, and indifferent to the world.” Langlands, in Mathematicians: An Outer View of the Inner World, p142. (From James Milne website)