# VERMEIRE, PETE

## Professor

ASSOC DEAN/SCIENCE & ENGINEERING

### Publications & Presentations

Publications

- "Betti Tables of Reducable Algebraic Curves," joint with David J. Bruce, Pin-Hung Kao, Evan D. Nash, and Ben Perez, to appear,
*Proc. Amer. Math. Soc*. (Updated 2/2/13) - "Line Arrangements Modeling Curves of High Degree: Equations, Syzygies and Secants," joint with Gregory Burnham, Zvi Rosen, and Jessica Sidman, submitted for publication. (Updated 1/9/12)
- "Arithmetic properties of the first secant variety to a projective variety", preprint. (Updated 10/12/10)
- "Generation and Syzygies of the First Secant Variety to a Smooth Curve",
*Proc. Amer. Math. Soc*. 140 (2012), pp. 2639-2646. - "Equations Defining Secant Varieties: Geometry and Computation", joint with Jessica Sidman, in Combinatorial Aspects of Commutative Algebra and Algebraic Geometry,
*Abel Symposia 6*, Springer-Verlag (2011), pp. 155-174. - "Syzygies of the Secant Variety of a Curve", joint with Jessica Sidman,
*Algebra and Number Theory 3*(2009), no. 4, pp. 445-465. - "An Effective Bound for Reflexive Sheaves on Canonically Trivial 3-folds", submitted for publication.
- "Singularities of Secant Varieties",
*Journal of Pure and Applied Algebra*213 (2009), pp. 1129-1132. - "Regularity and Normality of the Secant Variety to a Projective Curve",
*Journal of Algebra*319 (2008), pp. 1264-1270. - "Classes of Stable Complex Matrices Defined via the Theorems of Gershgorin and Lyapunov", joint with Bryan Cain, Terry Lenker, and Sivaram Narayan,
*Linear and Multilinear Algebra*56 (2008), no. 6, pp. 713-724. - "Reflexive Sheaves and Elliptic Curves on Smooth Fano 3-folds",
*Osaka Journal of Mathematics*45 (2008), no. 1, pp. 85-89. - "Moduli of Reflexive Sheaves on Smooth Projective 3-folds",
*Journal of Pure and Applied Algebra*211 (2007), pp. 622-632. - "Stable Reflexive Sheaves on Smooth Projective 3-folds",
*Pacific Journal of Mathematics*219 (2005), no.2, pp. 391-398. - "The Parity of Invariants of Coherent Sheaves on Smooth Three-Fold Hypersurfaces",
*Communications in Algebra*33 (2005), pp. 319-321. - "A Counter Example to Fulton's Conjecture on $\overline{M}_{0,n}$",
*Journal of Algebra*248 (2002), pp. 780-784. - "On the Regularity of Powers of Ideal Sheaves",
*Compositio Mathematica*, 131 (2002), no. 2, pp. 161-172. - "Secant Varieties and Birational Geometry",
*Mathematische Zeitschrift*242 (2002), no. 1, pp. 75-95. - "Some Results on Secant Varieties Leading to a Geometric Flip Construction",
*Compositio Mathematica*125 (2001), no. 3, pp. 263-282.

- "Generation and Syzygies of the First Secant Variety", Workshop on Algebraic Geometry, Universidad Complutense de Madrid, December 2009.
- "Arithmetic Properties of Secant Varieties", Series of lectures given at the Korean Advanced Institute of Science and Technology (KAIST), Daejon, S. Korea, March 2009.
- "Equations Defining Secant Varieties", special joint Commutative Algebra/Algebraic Geometry Seminar, University of Illinois, Champaign, IL, October 2008.
- "Regularity and Normality of Secant Varieties", invited special session address, 2008 AMS-MAA Annual Meeting, San Diego, CA, January 2008.
- "Geometry of Secant Varieties", Valley Geometry Seminar, University of Massachusetts, Amherst, MA, October 2007.
- "The Geography of Symplectic Fibrations", Colloquium, Oklahoma State University, Stillwater, OK, October 2006.
- "The Moduli of Rank 2 Reflexive Sheaves on Smooth 3-folds", 2005 AMS Summer Institute, Seattle WA, Summer 2005.

### Education

- Ph.D., University of North Carolina at Chapel Hill, 1998
- B.S., University of Notre Dame, 1992

### Research Interests

- Algebraic Geometry
- Commutative Algebra