Benjamin J. Howard

Institute for Mathematics and its Applications
University of Minnesota
400 Lind Hall
207 Church St. S.E.
Minneapolis, MN 55455-0436
Office: 432 Lind Hall
Phone: (612) 626-1880
Email: bhoward@ima.umn.edu

PhD Advisor: Dr. John Millson

Curriculum Vitae
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.
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