Writing

Talks

Here are the slides/notes for talks I have given during my PhD.

Lifting Problem for Curves (slides) (.pdf): given at the Graduate Center, CUNY, as part of the Mathematics Department Lightning Talks.

GAGA Theorems: Complex (.pdf), Formal (.pdf) and Rigid (.pdf): Talk was in three parts, and was a milestone in my advancement to candidacy. Topics were Serre's GAGA Theorem and it's analogues to Formal and Rigid Geometry. Talk was based on these notes of David Harbater, entitled Patching and Galois Theory.

Sheaf Cohomology I : Topological Spaces (.pdf): Talk given in an Algebraic Geometry learning seminar. Covers the basic ideas of sheaf cohomology on topological spaces.

Sheaf Cohomology II: Schemes and Varieties (.pdf): Talk given in an Algebraic Geometry learning seminar. Covers the basic ideas of sheaf cohomology applied to schemes, and introduces Cech cohomology.

Affine Geometric Invariant Theory (.pdf): Talk given as part of a geometric group theory class. Covers the basic ideas of affine GIT and linearly reductive groups.

Spectral Sequences (.pdf): Talk given in an Algebraic Geometry learning seminar. Covers the construction of spectral sequences from the theory of exact couples.

Expository Notes

Here is a collection of some notes I have written throughout graduate school. Some were written for seminars and some for my own use. I claim no originality for any of the material, except for any mistakes.

Function Fields of Integral Schemes (.pdf): notes on the construction of the function field of an integral scheme.

Complex Multiplication and Elliptic Curves (.pdf): notes on the theory of CM elliptic curves. Based on a talk given for a class field theory class.

Ètale Coverings and Galois Categories (.pdf): notes on Grothendieck’s theory of finite ètale coverings and the fundamental functor. Based on a talk given in Prof. Szpiro’s algebraic geometry class.

Weil Conjectures for Curves (.pdf): notes on Bombieri’s proof of the Hasse-Weil bound for curves. These are based on a talk I gave in Prof. Szpiro’s algebraic geometry class.