Publications

• A geometric invariant theory construction of moduli spaces of stable maps
  (with Elizabeth Baldwin)
  Intern. Math. Res. Papers (2008) Vol. 2008; article ID rpn004, 104 pages
   

• Geometric invariant theory and moduli spaces of pointed curves
  Ph.D dissertation, Columbia University, 2008. 134 pages
   

Preprints

• GIT stability of weighted pointed curves
  arXiv: 0801.1288, 41 pages (January 2008)
   

• Nef divisors on \bar{M}_{0,n} from GIT
  (with Valery Alexeev)
  arXiv: 0812.0778, 14 pages (Dec 2008)
   

Slides from talks

• Nef line bundles on \bar M_{0,n} from GIT
  
  Sogang University and Postech University, June 2009
   

• State polytopes and GIT
  
  Sogang University, June 2009
   

• Geometric invariant theory and moduli spaces of pointed curves
  
  Harvard/MIT algebraic geometry seminar, October 2008
   

• Equations of graph curves
  
  AMS regional meeting, Stevens Institute of Technology, April 2007
   

Work in progress

• Gröbner techniques for low degree Hilbert stability
  (with Ian Morrison)
  Here are the calculations and code samples.
   

Tutorials

• The Eichler trace formula for representations of automorphisms of curves
  "Light entertainment." --Ian Morrison
   

• Using Magma to study automorphisms of curves Text file with cut-and-paste commands
  Recent versions of Magma include functions that, given an ideal of a curve, will compute its automorphism group.  

• Code samples for computing state polytopes and studying representations of automorphism groups of curves. Code samples
   

Computing

• I wrote a package StatePolytope for Macaulay 2 which computes state polytopes. It's available through the M2 webpage. Documentation for the functions is installed along with the package. 

• Cf. the Magma tutorial on automorphisms of curves above  

• Cf. the calculations accompanying my preprint with Ian Morrison above