Alexandra Seceleanu

Teaching

• I will be on leave at the Mathematical Sciences Research Institute (MSRI). The best way to reach me is to send me an email. I will be back in Spring 2013.

Research and Publications

My research is in commutative algebra, with an interest in homological methods and connections to algebraic geometry.

1. Computations in intersection rings of flag bundles (with D. Grayson, M. Stillman)
2. Bounding projective dimension (with J. McCullough) - submitted
3. Syzygies and singularities of tensor product surfaces of bidegree (2,1) (with H. Schenck, J. Validashti) - submitted
4. Syzygy theorems via comparison of order ideals on a hypersurface (with P. A. Griffith) J. Pure Appl. Algebra 216 (2012), no. 2, 468-479.
5. Inverse systems, fat points and the weak Lefschetz property (with B. Harbourne and H. Schenck) J. Lond. Math. Soc. (2) 84 (2011), no. 3, 712-730.
6. Ideals with Large Projective Dimension and Regularity (with J. Beder, J. McCullough, L. Nunez-Betancourt, B. Snapp, B. Stone) J. Symbolic Comput. 46 (2011), no. 10, 1105-1113. Here is the Macaulay 2 code mentioned in the paper.
7. The Weak Lefschetz Property and powers of linear forms in K[x, y, z] (with H. Schenck) Proc. Amer. Math. Soc. 138 (2010), no. 7, 2335-2339.
   

Selected Talks

• Bounding projective dimension Algebra, Geometry and Combinatorics Day in Urbana-Champaign, Apr 2012
• A hands-on approach to tensor product surfaces (slides) AMS Sectional Meeting in Lawrence, Apr 2012
• Bounding projective dimension and regularity (slides) AMS Sectional Meeting in Lincoln, Oct 2011
• Fat points and the weak Lefschetz property (slides) International Congress of Romanian Mathematicians in Brasov, Jul 2011
• From syzygies to the weak Lefschetz property and back (slides) Resolutions Day at Cornell, May 2011
• Inverse systems, fat points and the weak Lefschetz property (slides) AMS Joint Mathematics Meeting in New Orleans, Jan 2011
• Syzygy theorem via comparison of order ideals (slides) AMS Joint Mathematics Meeting in San Francisco, Jan 2010
• Weak Lefschetz Property and powers of linear forms (slides) AMS Sectional Meeting in Boca Raton, Nov 2009
• Weak Lefschetz property for ideals generated by powers of linear forms (poster), PASI conference in Olinda, Aug 2009

Computer Algebra Projects

I have authored or co-authored several packages for the computer algebra program Macaulay2:

• GenericInitialIdeal
• Regularity
• SymmetricPolynomials
• BigIdeals

Links commalg.org MathSciNet via UIUC library MathSciNet via UNL library ArXiv Mathoverflow MSRI 2012 program