Benjamin J. Howard

Department of Mathematics
University of Michigan
2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043

Office: 1847 East Hall
Phone: 734-936-2879
Email: howardbj AT umich DOT edu
About me: I am an NSF postdoctoral fellow (DMS-0703674) and T.H. Hildebrandt Research Assistant Professor. In 2006, I graduated from the University of Maryland, College Park, under John Millson. Most of my research is about group actions on varieties or symplectic manifolds. My Curriculum vitae.
TEACHING
For Fall 2009, I'm teaching Math 215 (Multivariable Calculus), section 040, MWF 10-11. First day handout.

RESEARCH
"Matroids and Geometric Invariant Theory of torus actions on flag spaces", Journal of Algebra, vol. 312 (2007) no. 1, 527-541.
with John Millson, Andrew Snowden, and Ravi Vakil:

"The equations for the moduli space of n points on the line", Duke Math. J. 146 (2009), no. 2, 175--226. [Here we show that scheme-theoretically, if n is not six, then the equations for the moduli space of n points on the line is cut out by a certain set of quadratic equations]

"A description of the outer automorphism of S_6, and the invariants of six points in projective space", J. Combin. Theory Ser. A 115 (2008), no. 7, 1296--1303.

"The ring of projective invariants of eight points on the line via representation theory", arXiv:0809.1233 [We are working on, and intend to expand, this paper to include an interesting duality with the space of eight points in projective 3 space] Some code used for the eight point paper

"The relations among invariants of points on the projective line", Comptes rendus - Mathematique 347 (2009), pp. 1177-1182. [Here we announce and describe the main theorems of the paper below]

"The ideal of relations for the ring of invariants of n points on the line", arXiv:0909.3230. [Here we prove the conjecture that we made in the Duke paper that the full ideal of relations is generated by certain quadratic relations, as long as n is not six]

"The ideal of relations for the ring of invariants of n points on the line: integrality results", arXiv:0909.3242. [This paper shows that the results of the above paper (arXiv:0909.3230) also apply when working over Z[1/12!].]
with Chris Manon and John Millson: "The Toric Geometry of Triangulated Polygons in Euclidean Space", to be published in Canadian Journal of Mathematics (also at arXiv:0810.1352).
with Tyrrell McAllister: "Degree bounds for type-A weight rings and Gelfand--Tsetlin semigroups", submitted (also at arXiv:0812.0826).
with John Millson: "The Chevalley involution and a duality of weight varieties", Asian Journal of Math (Armand Borel Memorial Issue), Dec 2004.
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