Research

My research interests focus around algebraic groups, representation theory, and related algebraic geometry. I am particularly interested in the geometry of certain special varieties which arise in the study of representations of algebraic groups and the connections between geometry and algebra. These special varieties include Schubert varieties, nilpotent orbits (and their associated orbital varieties), and support varieties for modules over infinitesimal group schemes.

Publications

Peer Reviewed Journals

• Singular Chern Classes of Schubert Varieties via Small Resolution
  Accepted International Mathematics Research Notices. Preprint available at arXiv:0804.0202v1 [math.AG], (32 pages, 3 figures, 2 tables)
• Cohomology of Quantum Groups: An Analog of Kostant's Theorem (with UGA VIGRE Algebra Group)
  Accepted Proceedings of the American Mathematical Society. Preprint available at arXiv:0809.0838v1 [math.RT], (12 pages)

Preprints

• Support Varieties for Demazure Modules (with Daniel K. Nakano)
  Submitted, Preprint available at ...
• On the Wonderful Compactification (with Sam Evens)
  Preprint available at arXiv:0801.0456v1 [math.AG] (28 pages)
• On the Singular Chern Classes of Schubert Varieties via Small Resolution
  Ph.D. Thesis [PDF], (133 pages, 8 figures, 4 tables)
• Link to all my articles on the arXiv: http://arxiv.org/a/jones_b_1, (uses the new author identifier system).

In Preparation

• Normality of Enhanced Nilpotent Orbit Closures (with Pramod Achar and Anthony Henderson)
• Resolutions of Singularities for Mirabolic Orbit Closures

Reviews

• Book Review: Lie theory. Lie Algebras and Representations (with Brian C. Hall), Edited by Jean-Philippe Anker and Bent Orsted, articles by Jens Jantzen and Ker l-Hermann Neeb., SIAM Review, Vol. 47 no. 3, pp. 608 -- 610. September 2005.
  [link] (the link may only work if you have institutional access to SIAM Review)

Invited Talks

• Nov. 8, 2009: Slides: Support Varieties for Demazure Modules. AMS Western Sectional Meeting, Riverside CA (U.C. Riverside)
• Apr. 5, 2009: Slides: Computing Singular Chern Classes and Related Invariants for Schubert Varieties in a Grassmannian. AMS Southeast Sectional Meeting, Raleigh NC (NC State).
• Jan. 7, 2009: Slides: Normality of Enhanced Nilpotent Orbit Closures (Preliminary Report). AMS National Meeting, Washington D.C.
• Nov. 4, 2007: Slides: Singular Chern Classes of Schubert Cells and Varieties Via Small Resolution. AMS Southeastern Sectional Meeting, Murfreesboro TN.

Computational Projects

• CSM Classes in Sage coming soon..
• CSM Classes: Computing Chern-Schwartz-MacPherson classes in the Grassmannian using Maple
• Gap 4 (r4) Benchmarks