Notes

Notes on Riemann surfaces 

(These are mainly from my participation in a student reading group in the Summer of 2016, and have been revised since.)  

• • Abel's theorem and Jacobian varieties 

  • Uniformization theorem (including a proof and various applications)

The Thurston pullback map

• • Thurston's topological characterization of rational functions   (This note was initiated as the final project for a complex dynamics course in the Winter of 2017, and has been revised since.)

Some computations in the Grothendieck ring of varieties

• The motivic class and the orbifold Euler characteristic of the fixed-point marked moduli spaces of rational maps.