Mark E. Huibregtse, Professor of Mathematics, Skidmore College 

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Resume for Mark E. Huibregtse Date: 21 May 2018
Education:
· Institute for Retraining in Computer Science (IFRICS), Clarkson University, Potsdam, NY, June 1985  August 1986 (involved two intensive twomonth summer sessions with an intervening yearlong project).
·
Massachusetts Institute of Technology,
·
Teaching Experience:
·
·
·
Massachusetts Institute of Technology,
Publications:
1.
The Albanese Mapping for a Punctual Hilbert
Scheme:
2. The Albanese Mapping for a Punctual Hilbert Scheme: II. Symmetrized Differentials and Singularities, Transactions of the American Mathematical Society 274 (1982), 109140. MR 84h:14009 3. Translation by Torsion Points and Rational Equivalence of 0cycles on Abelian Varieties, Rocky Mountain Journal of Mathematics 18 (1988), 147155. MR 89j:14005 4. Local Properties of Secant Varieties in Symmetric Products, Part I, with Trygve Johnsen, Transactions of the American Mathematical Society 313 (1989), 187204. MR 89i:14025 5. Quotients of GStable Closed Subschemes, Cartesian Diagrams, and Closed Immersions, Rocky Mountain Journal of Mathematics 25 (1995), issue #4, 13571384. MR 97a:14048 6. Some Amplifications and a Correction of Iarrobino’s Construction of Local Parameters on Hilb^n_{P^2_k}, Rocky Mountain Journal of Mathematics 29 (1999), issue #4, 13211361. MR 2001c:14008 7. A Description of Certain Affine Open Subschemes that Form an Open Covering of Hilb^n_{A^2_k}, Pacific Journal of Mathematics 204 (2002), issue #1, 97143. MR 1 905 194 8. On Ellingsrud and Strømme’s cell decomposition of Hilb^{n}_{A^2_C}, Inventiones mathematicae 160 (2005), 165172. MR2129711 9. An elementary construction of the multigraded Hilbert scheme of points, Pacific Journal of Mathematics 223 (2006), no. 2, 269315. MR2221028
10.
Some
syzygies of the generators of the ideal of a border basis scheme, Collectanea Mathematica 62 (2011), issue #3, pages 341366. Initial publication is via the Web: http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s1334801000237 . Posted on the arXiv preprint server at arXiv:0908.0509. MR2825716 (2012g:13022)
11.
Envelope
curves and equidistant sets, with
Adam Winchell (Skidmore Class of 2016), Involve, a Journal of
Mathematics 9 (2016), no. 5, 839856. MR3541984 DOI 10.2140/involve.2016.9.839.
12.
Some
elementary components of the Hilbert scheme of points, Rocky Mountain Journal of Mathematics 47
(2017), issue #4, pages 11691225. DOI 10.1216/RMJ210741169. MR3689951. Posted on the arXiv preprint server at arXiv:1407.1440v2 [math.AG].
Unpublished
Manuscripts
1. The cotangent space at a monomial ideal of the Hilbert scheme of points of an affine space, written in summer 2004, revised spring 2005, and posted to the arXiv preprint server on 28 June 2005. ( arXiv:math/0506575 [math.AG] )
1.
Product
Schemes with Group Action and Secant Sheaves on Quotients, AMS Contributed
Paper Session, Orono, ME, August 1991.
2. Quotients of GStable Subschemes: Questions of Embedding and Cartesianness, a series of two talks given to the Capital Region Algebra and Number Theory Seminar, 29 October and 12 November 1991, Union College. 3. Quotients of GStable Subschemes, Cartesian Diagrams, and Embeddings, AMS Session on Algebraic Geometry and Applied Group Theory, San Antonio, TX, January 1993. 4. Symmetrized Differentials on Hilbert Schemes of Points, preliminary report, AMS Session on Algebraic Geometry, Cincinnati, OH, January 1994. 5. Symmetrized Differentials and Secant Sheaves on Hilbert Schemes of Points, AMS Session on Algebraic Geometry, San Francisco, CA, January 1995. 6. An expanded version of the previous talk was presented to the CRANTS seminar at Union College, March 1995. 7. The First Degeneracy Locus of the Map Sec(\Omega^1_X) à Sec(\Omega^1_{H^n_X}) for an Algebraic Surface X, AMS Session on Commutative Algebra and Algebraic Geometry, Orlando, FL, January 1996. 8. On the Tangent Space at a kpoint of Hilb^n_X for an Algebraic Surface X, AMS Session on Algebraic Geometry, San Diego, CA, January 1997. 9. An Introduction to Hilb^n_{A^2_k} and to Some of its Local Charts, Geometry, Algebra, and Topology (GAT) Seminar, Texas A&M University, 24 November 1997. 10. Some Amplifications and a Correction of Iarrobino’s Construction of Local Parameters on Hilb^n_{P^2_k}, AMS Session on Algebraic Geometry and Fields, Baltimore, MD, January 1998. 11. A Description of Certain Affine Open Subschemes That Form an Open Covering of Hilb^n_{A^2_k}, AMS Session on Algebraic Geometry, Joint AMSMAA Winter Meetings at San Antonio, TX, 15 January 1999. 12. Open subschemes of Hilb^n_{A^2_k} that are isomorphic to A^{2n}_k, AMS Session on Algebraic Geometry, Joint AMSMAA Winter Meetings at Washington, DC, 19 January 2000. 13. An elementary construction of certain affine open subschemes of the Hilbert scheme of n points of the affine plane (Preliminary report), AMS Session on Algebraic Geometry and Linear Algebra, Joint AMSMAA Winter Meetings at New Orleans, LA, 13 January 2001. 14. A description of certain affine open subschemes that form an open covering of the Hilbert scheme of n points of the affine plane, a series of two talks presented to the CRANTS seminar meeting at Union College, 7 and 21 March 2001. 15. An elementary construction of an open affine covering of the Hilbert scheme of points of an affine space, AMS Special Session on Hilbert Schemes, AMS Regional Meeting #979, Northeastern University, Boston, MA, 6 October 2002. 16. On Ellingsrud and Strømme's explicit description of a cell decomposition of the Hilbert scheme of points of the affine plane, AMS Session on Algebraic Geometry and Algebra, Joint AMSMAA Winter Meetings in Baltimore, MD, 17 January 2003. 17. The cotangent space at a monomial ideal of the Hilbert scheme of points of an affine space, AMS Session on Algebra, Joint AMSMAA Winter Meetings in Atlanta, GA, Wednesday, 5 January 2005. 18. An elementary construction of the Hilbert scheme of points of an affine space, Union College Occasional Mathematics Conference, 3 December 2005. 19. Smooth monomialideal points of the Hilbert scheme of points of an affine space, AMS Session on Algebraic Geometry, Joint AMSMAA Winter Meetings in San Antonio, TX, 13 January 2006. 20. An elementary construction of the Hilbert scheme of points of an affine space, presented to CRANTS seminar at Skidmore on 6 December 2006. 21. Some syzygies of the generators of the ideal of a border basis scheme, AMS Session on Algebraic Geometry and KTheory, Joint AMSMAA Winter Meetings in Washington, DC, 8 January 2009.
22.
Some
Elementary Components of the Hilbert Scheme of Points, AMS Session on Algebraic Varieties, Moduli
Spaces, and Singularities, AMSMAA Joint Mathematics Meetings in San Diego, CA,
12 January 2013.
23.
A
generalization of Emsalem and Iarrobino's construction of elementary components of the Hilbert scheme of points, AMS Special Session on Commuting Nilpotent Matrices and
the Hilbert Scheme, AMS Regional Meeting # 1088 at Chestnut Hill, MA, Sunday, 7
April 2013, 10:3010:50 a.m., talk # 10881489.
Other Presentations:
1. Choosing the kth Largest Element: a kth Study in Algorithm Design and Analysis, Skidmore Mathematics and Computer Science Colloquium, 17 November 1987. 2. ISETL and Mathematical Programming: Why Would I Settle For Less? Skidmore Mathematics and Computer Science Colloquium, 16 March 1989. 3. The Rise and Fall of Euclidean Geometry, MAA Special Session on Using History in the Teaching of Mathematics, San Francisco, CA, January 1991. 4. Served as panelist for a discussion: What is the Mathematical Research Experience? Regional Geometry Institute, Amherst College, July 1992. 5. An Explicit Computation of an Invariant Subring of a Polynomial Ring, Hudson River Undergraduate Mathematics Conference, Siena College, April 1994. 6. Demonstrating SpaceFilling Curves with Derive: A Cautionary Tale? Hudson River Undergraduate Mathematics Conference, Siena College, April 1995. 7. Mathematica Programming, presented as part of a departmental workshop on Mathematica, 31 May 2001. 8. The BanachTarski Paradox I: Preliminaries, Hudson River Undergraduate Mathematics Conference, Union College, April 2009. (This was an introduction to the talk by my thesis student Rozalina Zlatareva, titled The BanachTarski Paradox II: Outline of Proof.) 9. The MerkleHellman Cryptosystem, Hudson River Undergraduate Mathematics Conference, Keene State University, April 2010. 10. Equidistant sets of curves, Hudson River Undergraduate Mathematics Conference, St. Michael’s College, Colchester, VT, April 2016. 11. Elliptic Curves over Finite Extension Fields I: Preliminaries, Hudson River Undergraduate Mathematics Conference, Westfield State University, Westfield, MA, 8 April 2017. 12. Hilbert Schemes of Points: Introduction, Hudson River Undergraduate Mathematics Conference, St. Lawrence University, Canton, NY, 7 April 2018. 13. An Application of Desargues’ Theorem, Pi Mu Epsilon Induction Ceremony and Dinner, Skidmore College, 9 April 2018.
1.
American Association of University
Professors (AAUP).
2. American Mathematical Society (AMS).
3.
Mathematical Association of America
(MAA).
