Nonsingular Schubert Varieties dvi ps pdf
My final project for Bill Fulton's algebraic geometry class. It gives a description of which Schubert varieties are nonsingular in Grassmannians over the complex numbers. 2010

Homotopy Theory dvi ps pdf
Notes for a talk I gave as part of the PROMYS counselor seminar on algebraic topology. Material from J. P. May's A Concise Course in Algebraic Topology and Allen Hatcher's Algebraic Topology (awesome books). 2010

Growth of Subgroups of GL_n(R) dvi ps pdf
An inquiry-based learning worksheet written with Dylan Murphy for Miklos Abert. IBL worksheets introduce topics by giving definitions and problems (no proofs!) which makes them great for developing an understanding of new objects. This one covers some aspects of the Tits' alternative and growth of infinite groups. 2009

Complex Lie Algebras dvi ps pdf
My paper for the 2009 REU at the University of Chicago. This paper gives the beautiful classification of semi-simple Lie algebras over C (material from Introduction to Lie Algebras by Karin Erdmann and Mark J. Wildon). 2009

Delta-Hyperbolic Groups pdf
Another IBL worksheet written with a bunch of other UChicago students. This one outlines steps to showing that delta-hyperbolic groups have a finite presentation and solvable word problem. 2008

Amalgams, Graphs, and Free Groups pdf
Another IBL worksheet written with a bunch of other UChicago students. It outlines a proof of Schreier's Theorem and is mostly material from J. P. Serre's Trees . 2008