Pete Vermeire
Pete Vermeire
Professor
Associate Dean, College of Science and Technology

Algebraic Geometry

Pearce Hall 221
989-774-6521
p.vermeire@cmich.edu

Personal Web Page

Education

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

Affiliations

American Mathematical Society (AMS), Mathematics Association of America (MAA)

Honors and Awards

  • College of Science and Technology Award for Outstanding Teaching, 2006
  • Nominee: CMU teaching award, 2005, 2006
  • Nominee: Provost's Research Award, 2004

Research Areas

Algebraic Geometry and Commutative Algebra

Recent Publications and 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.

Recent Invited Presentations

  • "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.