___________________________________________________________________ Hal Schenck

Hal Schenck

Mathematics Department, 620B Blocker Building
Texas A&M University
College Station TX 77843
tel: 979-845-7792
fax: 979-862-4190

schenck@math.tamu.edu

___________________________________________________________________

Who am I?

I am an Associate Professor in the Mathematics Department at Texas A&M; in 2007-2008 I'm on leave of absence at University of Illinois. I completed my Ph.D. at Cornell in 1997, under the direction of Mike Stillman, and did postdoctoral work at Cornell, Harvard, and Northeastern. My research interests are in the areas of:

ocommutative algebra
oalgebraic geometry
odiscrete geometry and combinatorics
I'm especially interested in problems which can be studied from a computational standpoint, and in interactions of commutative algebra with problems in geometry and combinatorics, particularly applied problems. Among my current interests in applied algebraic geometry are surface modelling and coding theory. I also enjoy working on problems at the interface of discrete geometry and algebra; for example hyperplane arrangements (for an overview, you can watch my lecture at the MSRI introductory workshop on arrangements) and toric varieties. I've also worked on questions involving free resolutions, fatpoints, rational surfaces, Green's conjecture, stability and jump loci of vector bundles, and splines. I'm one of the organizers for the annual Texas Algebraic Geometry Seminar and am the faculty advisor to the Graduate student seminar. Here's my resume.
___________________________________________________________________

Information for students

For graduate students interested in commutative algebra and algebraic geometry, here are a few thoughts on what to read and how to choose an advisor. For a turbo introduction to algebraic geometry, you can check out notes from a course in Computational Algebraic Geometry that I taught at Harvard in fall 2000. For more advanced topics, check out Joe Harris's Second course in Algebraic Geometry and David Eisenbud's notes on The Geometry of Syzygies. Below are webpages of my students and postdocs:
___________________________________________________________________

Publications

o Betti numbers and degree bounds for some linked zero schemes, (joint with Leah Gold and Hema Srinivasan), Journal of Pure and Applied Algebra, 210, (2007), 481-491.
o A case study in bigraded commutative algebra, (joint with David Cox and Alicia Dickenstein), in "Syzygies and Hilbert Functions", edited by Irena Peeva, Lecture notes in Pure and Applied Mathematics 254, (2007), 67--112.
o Syzygies, multigraded regularity and toric varieties, (joint with Milena Hering and Gregory G. Smith), Compositio Mathematica, 142, (2006), 1499-1506.
o Toric surface codes and Minkowski sums, (joint with John Little), SIAM Journal on Discrete Mathematics, 20, (2006), 999-1014.
o Derivation modules of orthogonal duals of hyperplane arrangements, (joint with Joseph P.S. Kung), in Journal of Algebraic Combinatorics, 24, (2006), 253-262.
o Resonance, linear syzygies, Chen groups, and the Bernstein-Gelfand-Gelfand correspondence, (joint with Alex Suciu), in Transactions of the A.M.S., 358, (2006), 2269-2289.
o Cayley-Bacharach and evaluation codes on complete intersections, (joint with Leah Gold and John Little), in Journal of Pure and Applied Algebra, 196, (2005) p. 91-99.
o Linear systems on a special rational surface, in Mathematical Research Letters, 11, (2004) p. 697-714.
o Lattice polygons and Green's theorem, in Proceedings of the A.M.S., 132, (2004) p. 3509-3512.
o Elementary modifications and line configurations in P^2, in Commentarii Mathematici Helvetici, 78, (2003) p. 447-462.
o Local complete intersections in P^2 and Koszul syzygies, (joint with David Cox), in Proceedings of the A.M.S., 131, (2003) p. 2007-2014.
o Lower central series and free resolutions of hyperplane arrangements, (joint with Alex Suciu), in Transactions of the A.M.S., 354, (2002) p. 3409-3433.
o Cohomology vanishing and a problem in approximation theory, (joint with Peter Stiller), in Manuscripta Mathematica, 107, (2002) p. 43-58.
o The module of logarithmic p-forms of a locally free arrangement, (joint with Mircea Mustata), in Journal of Algebra, 241, (2001) p. 699-719.
o On a conjecture of Rose, (joint with John Dalbec), in Journal of Pure and Applied Algebra, 165, (2001) p. 151-154.
o A rank two vector bundle associated to a three arrangement, and its Chern polynomial, in Advances in Mathematics, 149, (2000) p. 214-229.
o Subalgebras of the Stanley-Reisner ring, in Discrete and Computational Geometry, 21, (1999) p. 551-556.
o Fat points, inverse systems, and piecewise polynomial functions, (joint with Anthony Geramita), in Journal of Algebra, 204, (1998) p. 116-128.
o A spectral sequence for splines, in Advances in Applied Mathematics, 19, (1997) p. 183-199.
o Local cohomology of bivariate splines, (joint with Mike Stillman), in Journal of Pure and Applied Algebra, 117-118, (1997) p. 535-548.
o A family of ideals of minimal regularity and the Hilbert series of C^r(\Delta), (joint with Mike Stillman), in Advances in Applied Mathematics, 19, (1997) p. 169-182.
___________________________________________________________________

Preprints

o Holonomy Lie algebras and the LCS formula for subarrangements of A_n, (joint with Paulo Lima-Filho).
___________________________________________________________________

Computational mathematics

oMacaulay2: A program for computing in commutative algebra and algebraic geometry.
oCoCoA: Another option for computing in commutative algebra and algebraic geometry.
oPorta (and others): Programs for polyhedral geometry.
oSingular: A program for computations in local rings and singularities.
oSchubert: A program for enumerative geometry.
oSplinetool: Macaulay2 script which builds the chain complexes and allows computation of various homology modules associated to splines.
oArrangetool: Macaulay2 script for computations involving three arrangements.
___________________________________________________________________

Sites I visit frequently

o ams web page
o siam web page
o New York times web page
o Algebraic Geometry preprints
oMSRI (Berkeley).
___________________________________________________________________