- Ph.D. in Mathematics, May 2009
- M.Phil. in Mathematics, February 2006
- M.A. in Mathematics, May 2004
University of Notre Dame:
- B.S. in Mathematics, magna cum laude, May 2002
Algebra and Algebraic Geometry
Combinatorial Commutative Algebra
My main research interest is combinatorial commutative algebra with a focus on free resolutions of monomial ideals, and toric ideals. I am also interested in connections to algebraic geometry and tropical geometry.
- "Rigid monomial ideals", preprint, arXiv:1102.2243
- "Finite atomic lattices and resolutions of monomial ideals", preprint, arXiv:1009.1430v1.
- "Finite atomic lattices and their relationship to resolutions of monomial ideals", Ph.D. Thesis, Columbia University, May 2009.
- "Constructing almost excellent unique factorization domains" (with John Bryk, Charles Samuels, Grace Wang), Communications in Algebra 2005 33 (5) 1321-1336.