Henry K. Schenck
Department of Mathematics
University of Illinois
Urbana, Illinois, 61801
tel: 217-333-2229
fax: 217-333-9576
schenck@math.uiuc.edu

Professional Experience

University of Illinois.
Department of Mathematics
Associate Professor, 2007-present.

Texas A&M University.
Department of Mathematics
Associate Professor, 2005-present.
Assistant Professor, 2001-2005.

Harvard University.
Department of Mathematics
NSF postdoctoral research fellow, 2000-2001.

Northeastern University.
Department of Mathematics
NSF postdoctoral research fellow, 1998-2000.

Cornell University.
Department of Mathematics
Visiting Assistant Professor, 1997-1998.

Education

Cornell University, Ithaca, NY.
Ph.D. in Mathematics, 1997.
M.S. in Mathematics, 1994.

Carnegie-Mellon University, Pittsburgh, PA.
B.S. in Applied Mathematics and Computer Science, 1986.

Books

"Computational Algebraic Geometry'',
Cambridge University Press, (2003).

Research Publications

"Betti numbers and degree bounds for some linked zero-schemes'', (with L. Gold and H. Srinivasan)
Journal of Pure and Applied Algebra, 210, (2007), 481-491.

"A case study in bigraded commutative algebra'', (with D. Cox and A. Dickenstein)
in "Syzygies and Hilbert Functions'', I. Peeva, ed., Lecture notes in Pure and Applied Mathematics 254, (2007), 67--112.

"Syzygies, multigraded regularity and toric varieties'', (with M. Hering and G. Smith)
Compositio Mathematica, 142, (2006), 1499-1506.

"Toric surface codes and Minkowski sums'', (with J. Little)
SIAM Journal on Discrete Mathematics, 20, (2006), 999-1014.

"Derivation modules of orthogonal duals of hyperplane arrangements'', (with J.P.S. Kung)
Journal of Algebraic Combinatorics, 24, (2006), 253-262.

"Linear syzygies, Chen ranks, and the Bernstein-Gelfand-Gelfand correspondence'', (with A. Suciu)
Transactions of the A.M.S., 358, (2006), p. 2269-2289.

"Cayley-Bacharach and evaluation codes on complete intersections'', (with L. Gold and J. Little)
Journal of Pure and Applied Algebra, 196, (2005) p. 91-99.

"Linear systems on a special rational surface'',
Mathematical Research Letters, 11, (2004) p. 697-714.

"Lattice polygons and Green's theorem'',
Proceedings of the A.M.S., 132, (2004) p. 3509-3512.

"Elementary modifications and line configurations in P^2'',
Commentarii Mathematici Helvetici, 78, (2003) p. 447-462.

"Local complete intersections in P^2 and Koszul syzygies'', (with D. Cox)
Proceedings of the A.M.S., 131, (2003) p. 2007-2014.

"Lower central series and free resolutions of hyperplane arrangements'', (with A. Suciu)
Transactions of the A.M.S., 354, (2002) p. 3409-3433.

"Cohomology vanishing and a problem in approximation theory'', (with P. Stiller)
Manuscripta Mathematica, 107, (2002) p. 43-58.

"The module of logarithmic p-forms of a locally free arrangement'', (with M. Mustata)
Journal of Algebra, 241, (2001) p. 699-719.

"On a conjecture of Rose'', (with J. Dalbec)
Journal of Pure and Applied Algebra, 165, (2001) p. 151-154.

"A rank two vector bundle associated to a three arrangement, and its Chern polynomial'',
Advances in Mathematics, 149, (2000) p. 214-229.

"Subalgebras of the Stanley-Reisner ring'',
Discrete and Computational Geometry, 21, (1999) p. 551-556.

"Fat points, inverse systems, and piecewise polynomial functions'', (with A. Geramita)
Journal of Algebra, 204, (1998) p. 116-128.

"A spectral sequence for splines'',
Advances in Applied Mathematics, 19, (1997) p. 183-199.

"Local cohomology of bivariate splines'', (with M. Stillman)
Journal of Pure and Applied Algebra,117-118, (1997) p. 535-548.

"A family of ideals of minimal regularity and the Hilbert series of C^r(Delta)'', (with M. Stillman)
Advances in Applied Mathematics, 19, (1997) p. 169-182.

Lectures and Presentations

"Algebra and geometry of four sections of O(2,1)'',
MFO miniworkshop on surface modelling and syzygies, Oberwolfach, November 2007.

"A syzygy approach to projective normality'',
MFO miniworkshop on projective normality of smooth toric varieties, Oberwolfach, August 2007.

"Splines on polyhedral complexes",
BIRS workshop on Commutative Algebra, Banff, Canada, June 2007.

"Syzygies of plane curve singularities",
MSRI workshop on Advances in Algebra and Geometry, Berkeley, April 2007.

"Toric surface codes and Minkowski sums",
AMS Special Session on low dimensional varieties, New Orleans, LA, January 2007.

"A spectral sequence stratification of cohomology jump loci",
AMS Special Session on Arrangements and related topics, New Orleans, LA, January 2007.

"Configurations of smooth rational curves in P^2",
BIRS workshop on Hilbert functions and Syzygies, Banff, Canada, October 2006.

"Fitting ideals and cohomology jump loci",
MSRI workshop on Configuration Spaces and Arrangements, Berkeley, August 2006.

"R^k for a k-generic arrangement is V(ann(Ext^{k+1}(F(A),S))), "
BIRS Focussed research group on complex arrangements, Banff, Canada, June 2006.

"Holonomy Lie algebras, Graphic Arrangements, and Tor_i^A(k,k)_i,"
AMS Special Session on Syzygies, San Antonio, TX, January 2006.

"Bigraded algebra and incomplete linear systems on P^1 x P^1",
AMS Special Session on Resolutions, Eugene, OR, November 2005.

"Projective dimension and derivations'',
PIMS workshop on Hyperplane Arrangements, Vancouver, Canada, August 2005.

"Syzygies and toric varieties'',
BASCOLA: Coloquio de Algebra en Buenos Aires, Buenos Aires, Argentina, August 2005.

"Holonomy Lie algebras and the LCS formula for graphic arrangements'',
XVI Coloquio Latinoamericano de Algebra, Colonia, Uruguay, August 2005.

"A spectral sequence stratification of cohomology jump loci''.
BIRS Focussed research group on cohomology and rational homotopy, Banff, Canada, June 2005.

"Commutative and homological methods for arrangements'',
MSRI Program on Hyperplane Arrangements, Berkeley, August 2004.

"Ideals of monomials and ideals of powers of linear forms'',
MFO workshop on commutative algebra and combinatorics, Oberwolfach, July 2004.

"Chen ranks and the Bernstein-Gelfand-Gelfand correspondence'',
Geometry-Combinatorics workshop, Flagstaff, January 2004.

"Linear systems on a special rational surface'',
AMS Special Session on Algebraic Geometry, Boulder, October 2003.

"Castelnuovo-Mumford regularity and line configurations in the projective plane'',
AMS Special Session on Combinatorial Commutative Algebra and Algebraic Geometry, San Francisco, May 2003.

"Hyperplane arrangements, free resolutions, and Bernstein-Gelfand-Gelfand'',
MSRI workshop on Computational Commutative Algebra, Berkeley, March 2003.

"Hyperplane arrangements and free resolutions'',
Contemporary Algebra and Algebraic Geometry conference, Texas Tech University, November 2002.
Symbolic Computational Algebra - Fields Institute special meeting, London, Ontario July 2002.

"Resonance Varieties and free resolutions'',
MFO workshop on Cohomology Jumping Loci, Oberwolfach, March 2002.

"Local complete intersections in P^2 and Koszul syzygies'',
AMS Special Session on Computational Algebraic Geometry, San Diego, January 2002.
Annapolis Algebraic Geometry conference, USNA, October 2001.

"A formula of Solomon-Terao and vector bundles on P^n'',
AMS Special Session on Commutative Algebra, New York, November 2000.

"Cohomology vanishing and a problem in approximation theory'',
AMS Special Session on Algebraic Geometry, Toronto, September 2000.

"Stability and jump loci of a family of bundles on P^2'',
AMS Special Session on Hyperplane Arrangements, New York, November 2000.
Aspects of Algebraic Geometry and Commutative Algebra, Texas A&M, May 2000.
AMS Special Session on Syzygies, Lowell, April 2000.

"Logarithmic p-forms on a locally free arrangement'',
Arrangements in Boston, Boston, June 1999.

"The Chern polynomial of a three arrangement'',
MSRI Workshop on computational methods in algebra and geometry, Berkeley, October 1998.
AMS Special Session on Commutative Algebra, Chicago, September 1998.

"Subalgebras of the Stanley-Reisner ring'',
AMS Special Session on Commutative Algebra, Montreal, September 1997.

"A spectral sequence for splines'',
Conference on Commutative Algebra and Combinatorics, Essen, Germany, June 1997.
MSRI workshop on Geometric Combinatorics, Berkeley, February 1997.

"Homological methods in the theory of splines'',
AMS Special Session on Computational Algebraic Geometry, San Diego, January 1997.

"Local cohomology of bivariate splines'',
Fourth International Symposium on Effective Methods in Algebraic Geometry, Eindhoven, Netherlands, June 1996.

Colloquium talks at Amherst, Georgia, Illinois, Navy, Nebraska, New Hampshire, Notre Dame, Rice, Texas A&M, TCU, UNC-Charlotte, UT-Arlington.

Seminar talks at Cornell, Georgia, Harvard, Illinois, Minnesota, MIT, Nebraska, New Hampshire, Northeastern, Notre Dame, Queens, Texas A&M, TCU, U. Mass., UC-San Diego, UNC-Charlotte, UT-Austin.

Academic Awards and Honors, Grants

NSF grant (Surface modeling, approximation theory, and coding theory), 8/15/07-7/30/10.
NSA grant (Applied commutative algebra), 1/1/07-1/1/09.
NSF grant (Symbolic computations in algebra and topology), 7/1/03-6/30/06.
NSA grant (Texas algebraic geometry conference), 5/1/06-6/1/06.
ATP grant (Non-standard splines for geometric modeling), 1/1/04-1/1/06.
NSA grant (Algebra and combinatorics of line arrangements in P^2), 1/1/03-1/1/05.
NSF grant (CBMS conference grant), 6/1/02-11/30/02.
NSF grant (Postdoctoral research fellowship) 9/1/98-8/31/01.
Postdoctoral research fellowship, MSRI, 1998 (declined).
Clark distinguished teaching award, Cornell University, 1997.
Graduate fellowship,Mathematical Sciences Institute, 1995.

Military

Officer, United States Army (1986-90). Left service as a Captain.
Awards and Decorations: ROTC Scholarship, Parachutist Badge, Expert Field Medical Badge,
Meritorious Service Medal, Army Commendation Medal, Overseas Service Ribbon.

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