I work in algebraic geometry. My current work focuses on abelian varieties, compactified Jacobians, moduli of sheaves and related topics.

During college, I worked at the Ross Mathematics Program at the Ohio State University for several summers. The program is a six week long residential program for high school students. I highly recommend the program! It is an excellent experience for talented students interested in mathematics.

Research Papers

• Singular curves and their compactified Jacobians
  To appear in conference proceedings for The view from Joe's Office: a celebration of algebraic geometry. (1 March, 2013)
• An Explicit Non-smoothable Component of the Compactified Jacobian
  Journal of Algebra, 370 (2012), 326-343.
• The Local Structure of Compactified Jacobians: Deformation Theory (with S. Casalaina-Martin and F. Viviani)
  Submitted. (21 July, 2011)
• Moduli of Generalized Line Bundles on a Ribbon (with D. Chen )
  Submitted. (June 27, 2011)
• The geometry and combinatorics of cographic toric face rings (with S. Casalaina-Martin and F. Viviani)
  To appear in Algebra & Number Theory. (Nov 22, 2011)
• Two ways to degenerate the Jacobian are the same.
  Algebra & Number Theory 7.2 (2012) 379-404.
• A Riemann Singularity Theorem for Integral Curves (with S. Casalaina-Martin.)
  American Journal of Mathematics, 134.5 (2012) 1143-1165.
• Good Completions of Néron Models
  Ph. D. Thesis. (2009)

I am not teaching right now.

When I was a graduate student, I had the honor of being a course assistant for the 7th most ridiculous-sounding math class offered at a liberal-arts college. The movie trailer for the class can be found here.

• Degenerating the Jacobian
  A poster I presented at the conference The View from Joe's Office. (Aug 28, 2011)
• Local Structure of Compactified Jacobians
  Slides from a talk I gave at the 2011 Joint Meetings. (Jan 7, 2011. Updated April 15, 2011)
• The Chow Ring of a Blow-up
  A short note explaining how to compute the Chow Ring of a simple blow-up. (Winter 2010)
• A Non-Reduced Picard Scheme
  A note describing Igusa's example of a surface with non-reduced Picard scheme. (March 2008)
• Notes on Néron Models
  Notes on Néron models for a talk that I gave in a student seminar. (Fall 2007)
• Notes on Compactified Jacobians
  Notes on compactified Jacobians for a talk that I gave in a student seminar. (Fall 2007)
• Notes on Abelian Schemes
  Notes on abelian schemes. Related exercises can be found at the botton of this webpage. (Summer 2005)
• Notes on Dieudonne modules
  Notes on Dieudonne modules. Based on another one of Brian's talks. (Summer 2005)