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
Professor, 2008.
Associate Professor, 2005-2008.
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.

Academic Awards and Honors, Grants

NSF grant (Combinatorial commutative algebra), 2011-2014.
NSA grant (Toric varieties, Hyperplane arrangements, Splines), 2011-2013.
NSF grant (Surface modeling, approximation theory, and coding theory), 2007-2010.
NSA grant (Applied commutative algebra), 2007-2009.
NSF grant (Symbolic computations in algebra and topology), 2003-2006.
NSA grant (Texas algebraic geometry conference), 2006.
Departmental outstanding service award, Texas A&M University, 2006.
ATP grant (Non-standard splines for geometric modeling), 2004-2006.
NSA grant (Algebra and combinatorics of line arrangements in P^2), 2003-2005.
NSF grant (CBMS conference grant), 2002.
NSF grant (Postdoctoral research fellowship) 1998-2001.
Postdoctoral research fellowship, MSRI, 1998 (declined).
College of Arts and Sciences, Cornell University: Clark distinguished teaching award, 1997.
Graduate fellowship,Mathematical Sciences Institute, 1995.

Service

Editorial Boards and National Committees
Managing Editor, Journal of Commutative Algebra, (2008-present).
Editorial Board, International Journal of Algebra and Computation, (2011-present).
Member, AMS Mathematical Research Community Advisory board (2008-present).

Departmental
Postdoctoral Committee, UIUC Math (chair, 2011-present).
Executive Committee, UIUC Math (2009-2011).
Graduate Affairs Committee UIUC Math (2008-2009, chair spring 2009).
Executive Committee, Texas A&M Math (2005-2007).
Committee to redesign Engineering Linear Algebra, Texas A&M Math (2006, chair).

Conference Organization
Scientific Committee, PIMS conference: "Arrangements and applications", Vancouver, Canada, August 2011.
Scientific Committee, MSRI-INdAM workshop "Toric Varieties", Cortona, Italy, July 2011.
Organizer, MSRI summer graduate student workshop "Toric Varieties", Berkeley, CA, June 2009.
Organizer, AMS-NSF Math Research Community workshop "Computational algebra and convexity", Snowbird, UT, June 2008.
Organizer, Oberwolfach Miniworkshop "Surface modelling", Oberwolfach, November 2007.
Organizer, Banff Focussed Research Group "Complex Arrangements", Banff, June 2006.
Organizer, Texas Algebraic Geometry Conference (NSA supported), Texas A&M University, May 2006.

Graduate Student and Postdoctoral Advising
Michael Dipasquale, current (UIUC)
Jimmy Shan, current (UIUC)
Alexandra Seceleanu, Ph.D. 2011 (UIUC)
Jimmy Kimball, Ph.D. 2008 (Texas A&M)
Stefan Tohaneanu, Ph.D. 2007 (Texas A&M)
Terry McDonald, Ph.D. 2006 (Texas A&M)
Javid Validashti, postdoc 2011-2012 (UIUC)
Leah Gold, NSF-Vigre postdoc 2002-2005 (Texas A&M)

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.

Publications

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

"Toric varieties", (with D. Cox, J. Little)
AMS Graduate Studies in Mathematics, (2011).

Research Papers
"High rank linear syzygies on low rank quadrics", (with M. Stillman)
American Journal of Mathematics, to appear.

"Toric Hirzebruch-Riemann-Roch via Ishida's theorem on the Todd genus",
Proceedings of the A.M.S., to appear.

"Local cohomology of logarithmic forms", (with G. Denham, M. Schulze, M. Wakefield, U. Walther)
Annales de l'Institut Fourier, to appear.

"Equivariant Chow cohomology of nonsimplicial toric varieties",
Transactions of the A.M.S., 364 (2012) 4041-4051.

"Hyperplane Arrangements: Computations and Conjectures",
Advanced Studies in Pure Mathematics, 62 (2012) 323-358.

"Resonance varieties via blowups of P^2 and scrolls",
International Math Research Notices, 20 (2011) 4756-4778.

"Inverse systems, Gelfand-Tsetlin patterns, and the weak Lefschetz property", (with B. Harbourne, A. Seceleanu)
Journal of the L.M.S., 84, (2011) 712-730.

"Euler characteristic of coherent sheaves on simplicial torics via the Stanley-Reisner ring",
Journal of Mathematical Physics, 51, (2010) doi 112304.

"The weak Lefschetz property and powers of linear forms in K[x,y,z]", (with A. Seceleanu)
Proceedings of the A.M.S., 138 (2010) 2335-2339.

"Freeness of Conic-Line arrangements in P^2'', (with S. Tohaneanu)
Commentarii Mathematici Helvetici, 84 (2009) 235-258.

"Piecewise polynomials on polyhedral complexes'', (with T. McDonald)
Advances in Applied Mathematics, 42 (2009), 82-93.

"The Orlik-Terao algebra and 2-formality'', (with S. Tohaneanu)
Mathematical Research Letters 16 (2009), 171-182.

"Holonomy Lie algebras and the LCS formula for subarrangements of A_n'', (with P. Lima-Filho)
International Math Research Notices, 8 (2009) 1421-1432.

"Efficient computation of resonance varieties via Grassmannians" (with P. Lima-Filho),
Journal of Pure and Applied Algebra, 213 (2009), 1606-1611.

"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

"Syzygies and toric varieties'',
MFO workshop on toric geometry, Oberwolfach, Germany, 4/12.

"Splines, spectral sequences, and polyhedral complexes'',
SIAM special session on geometric modelling, Raleigh, 10/11.

"Resonance varieties via blowups of P^2 and scrolls'',
AMS special session on algebraic geometry of arrangements, Worcester, 4/11.

"The weak Lefschetz property and powers of linear forms'',
KUMUNU Conference on commutative algebra, University of Nebraska, 4/11.

"Cohomology and Chow rings of toric varieties'',
BIRS workshop on Topological methods in toric and symplectic geometry, Banff, Canada, 11/10.

"Linear series and linear syzygies'',
MFO miniworkshop on Linear series on algebraic varieties, Oberwolfach, Germany, 10/10.

"Equivariant Chow cohomology of nonsimplicial toric varieties'',
Configuration Spaces: Geometry, Combinatorics and Topology, Centro de Giorgi, Pisa, Italy, 6/10.
AMS special session on zonotopal algebra, San Francisco, 1/10.

"Arrangements and Computations'' (series of 3 one-hour lectures),
Math Society of Japan summer school on Arrangements, Hokkaido, Japan, 8/09.

"Logarithmic forms for quasihomogeneous curve configurations in P^2'',
AIM squares workshop on Logarithmic forms, arrangements and D-modules, Palo Alto, 5/09.

"Toric specializations of the Rees algebra of Koszul cycles'',
AMS special session on algebra and number theory with polyhedra, San Francisco, 4/09.

"Piecewise polynomials on polyhedral complexes'',
Conference on algebraic geometry and approximation theory, Towson, MD, 4/09.

"Geometry and syzygies of surfaces associated to line configurations in P^2'',
Bluegrass Algebra Conference, University of Kentucky, 3/09.

"The Orlik-Terao algebra and 2-formality'',
Fields Institute conference in honor of Peter Orlik, Toronto, 8/08.

"Open problems on Hilbert functions and syzygies'',
AMS-NSF Mathematical Research Community Workshop, Snowbird, 6/08.

"Computational algebra and problems in algebraic topology and numerical analysis'',
Cornell Conference on Macaulay2, Ithaca 3/08.

"Algebra and geometry of four sections of O(2,1)'',
MFO miniworkshop on surface modelling and syzygies, Oberwolfach, Germany, 11/07.

"A syzygy approach to projective normality'',
MFO miniworkshop on projective normality of smooth toric varieties, Oberwolfach, Germany, 8/07.

"Splines on polyhedral complexes",
BIRS workshop on Commutative Algebra, Banff, Canada, 6/07.

"Syzygies of plane curve singularities",
MSRI workshop on Advances in Algebra and Geometry, Berkeley, 4/07.

"Toric surface codes and Minkowski sums",
AMS Special Session on low dimensional varieties, New Orleans, LA, 1/07.

"A spectral sequence stratification of cohomology jump loci",
AMS Special Session on Arrangements and related topics, New Orleans, LA, 1/07.

"Configurations of smooth rational curves in P^2",
BIRS workshop on Hilbert functions and Syzygies, Banff, Canada, 10/06.

"Fitting ideals and cohomology jump loci",
MSRI workshop on Configuration Spaces and Arrangements, Berkeley, 8/06.

"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, 6/06.

"Holonomy Lie algebras, Graphic Arrangements, and Tor_i^A(k,k)_i,"
AMS Special Session on Syzygies, San Antonio, TX, 1/06.

"Bigraded algebra and incomplete linear systems on P^1 x P^1",
AMS Special Session on Resolutions, Eugene, OR, 11/05.

"Projective dimension and derivations'',
PIMS workshop on Hyperplane Arrangements, Vancouver, Canada, 8/05.

"Syzygies and toric varieties'',
BASCOLA: Coloquio de Algebra en Buenos Aires, Buenos Aires, Argentina, 8/05.

"Holonomy Lie algebras and the LCS formula for graphic arrangements'',
XVI Coloquio Latinoamericano de Algebra, Colonia, Uruguay, 8/05.

"A spectral sequence stratification of cohomology jump loci''.
BIRS Focussed research group on cohomology and rational homotopy, Banff, Canada, 6/05.

"Commutative and homological methods for arrangements'',
MSRI Program on Hyperplane Arrangements, Berkeley, 4/04.

"Ideals of monomials and ideals of powers of linear forms'',
MFO workshop on commutative algebra and combinatorics, Oberwolfach, 4/04.

"Chen ranks and the Bernstein-Gelfand-Gelfand correspondence'',
Geometry-Combinatorics workshop, Flagstaff, 1/04.

"Linear systems on a special rational surface'',
AMS Special Session on Algebraic Geometry, Boulder, 10/03.

"Castelnuovo-Mumford regularity and line configurations in the projective plane'',
AMS Special Session on Combinatorial Commutative Algebra and Algebraic Geometry, San Francisco, 5/03.

"Hyperplane arrangements, free resolutions, and Bernstein-Gelfand-Gelfand'',
MSRI workshop on Computational Commutative Algebra, Berkeley, 3/03.

"Hyperplane arrangements and free resolutions'',
Contemporary Algebra and Algebraic Geometry conference, Texas Tech University, 11/02.
Symbolic Computational Algebra - Fields Institute special meeting, London, Ontario 7/02.

"Resonance Varieties and free resolutions'',
MFO workshop on Cohomology Jumping Loci, Oberwolfach, 3/02.

"Local complete intersections in P^2 and Koszul syzygies'',
AMS Special Session on Computational Algebraic Geometry, San Diego, 1/02.
Annapolis Algebraic Geometry conference, USNA, 10/01.

"A formula of Solomon-Terao and vector bundles on P^n'',
AMS Special Session on Commutative Algebra, New York, 11/00.

"Cohomology vanishing and a problem in approximation theory'',
AMS Special Session on Algebraic Geometry, Toronto, 9/00.

"Stability and jump loci of a family of bundles on P^2'',
AMS Special Session on Hyperplane Arrangements, New York, 11/00.
Aspects of Algebraic Geometry and Commutative Algebra, Texas A&M, 5/00.
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, UC-Riverside, UNC-Charlotte, U. North Texas, UT-Arlington, Western Illinois, U. Western Ontario.

Seminar talks at Cornell, Georgia, Harvard, Illinois, Minnesota, MIT, Nebraska, New Hampshire, Northeastern, Notre Dame, Purdue, Queens, Texas A&M, TCU, UIUC, UIC, UMass, UC-Riverside, UC-San Diego, UNC-Charlotte, U. North Texas, UT-Austin, U. Western Ontario, Wisconsin.

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