Benjamin J. Howard

Mathematics Department
University of Maryland
College Park, MD 20742
Office: 4308 Math Building
Email: bhoward@math.umd.edu

Advisor: Dr. John Millson

Curriculum Vitae
Research Statement

ArXiv links to recent papers:

Benjamin J. Howard:
Matroids and Geometric Invariant Theory of torus actions on flag spaces

In the paper "The projective invariants of ordered points on the line" we find generators for the ideal of relations in the projective invariants of n ordered points on the projective line (Alfred B. Kempe (1894) discovered that the lowest degree invariants generate). We find that the relations are generated by the relations of degree four and less. The relations we find are not as satisfactory as we would like them to be, however, since we chose a linearly independent set of generators, thus disrupting possible symmetries. Practically one must use a computer to list them all. The second paper, "The moduli space of n points on the line is cut out by quadrics when n is not six", is about a very simple and symmetric set of relations (they are linear and quadric) that cut out the moduli space scheme-theoretically, except for the case of six points, where one needs a cubic relation. We conjecture that these simple relations also generate the ideal.

Benjamin J. Howard, John J. Millson, Andrew Snowden, and Ravi Vakil:
The projective invariants of ordered points on the line

Benjamin J. Howard, John J. Millson, Andrew Snowden, and Ravi Vakil:
The moduli space of n points on the line is cut out by quadrics when n is not six

Benjamin J. Howard and John J. Millson:
The Chevalley involution and a duality of weight varieties
Asian Journal of Math (Armand Borel Memorial Issue), Dec 2004.