Research

My area of research is commutative algebra and algebraic geometry (MSC 13 and 14).

I am interested in a range of problems involving commutative algebra and algebraic geometry, usually with a combinatorial or computational flavor, such as: computing rank (especially Waring rank), secant varieties, and Hilbert functions; arrangements (of hyperplanes, lines, points, etc); multiplier ideals (computation, applications to commutative algebra); and computer experimentation in mathematics.

My dissertation was titled "Multiplier Ideals of Line Arrangements". I computed the multiplier ideals of general arrangements of lines through the origin in C^3, and even for "most" special arrangements. I studied under Rob Lazarsfeld at University of Michigan.

Me on ArXiv, me on MathSciNet, me on ORCID. Gallery of selected works.

Publications

  1. Mats Boij, Zach Teitler, A bound for the Waring rank of the determinant via syzygies, Linear Alg. Appl. 587 (2020), 195--214
  2. Brian Harbourne, Juan Migliore, Uwe Nagel, Zach Teitler, Unexpected hypersurfaces and where to find them, Michigan Math. J., to appear
  3. Jarosław Buczyński, Kangjin Han, Massimiliano Mella, Zach Teitler, On the locus of points of high rank, European J. Math. 4 (2018), no. 1, 113--136
  4. Theodosios Douvropoulos, Joachim Jelisiejew, Bernt Ivar Utstøl Nødland, Zach Teitler, The Hilbert scheme of 11 points in A^3 is irreducible. In Combinatorial Algebraic Geometry, 321--352, Fields Inst. Commun., 80, Fields Inst. Res. Math. Sci., Toronto, ON, 2017
  5. Zach Teitler, Sufficient conditions for Strassen's additivity conjecture, Illinois J. Math. 59 (2015), no. 4, 1071--1085
  6. Jarosław Buczyński, Zach Teitler, Some examples of forms of high rank, Collect. Math. 67 (2016), no. 3, 431--441
  7. Nathan Ilten, Zach Teitler, Product ranks of the $3 \times 3$ determinant and permanent, Canad. Math. Bull. 59 (2016), no. 2, 311--319
  8. Harm Derksen, Zach Teitler, Lower bound for ranks of invariant forms, JPAA 219 (2015), no. 12, 5429--5441
  9. Kent M. Neuerburg, Zach Teitler, Decompositions of ideals of minors meeting a submatrix, Comm. Alg. 44 (2016), no. 4, 1809--1820
  10. Nickolas Hein, Christopher J. Hillar, Abraham Martín del Campo, Frank Sottile, Zach Teitler The monotone secant conjecture in the real Schubert calculus, Exp. Math. 24 (2015), no. 1, 261--269
  11. Grigoriy Blekherman, Zach Teitler, On maximum, typical, and generic ranks, Math. Ann. 362 (2015), no. 3--4, 1021--1031
  12. Erik Holmes, Paul Plummer, Jeremy Siegert, Zach Teitler, Maximum Waring ranks of monomials and sums of coprime monomials, Comm. Alg. 44 (2016), no. 10, 4212--4219
  13. Weronika Buczyńska, Jarosław Buczyński, Johannes Kleppe, Zach Teitler, Apolarity and direct sum decomposability of polynomials, Michigan Math. J. 64 (2015), no. 4, 675--719.
  14. Zach Teitler, Software for multiplier ideals, JSAG 7 (2015), no. 1, 1--8
  15. Zach Teitler, Alexander Woo, Power sum decompositions of defining equations of reflection arrangements, J. Alg. Comb. 41 (2015), Issue 2, 365--383
  16. Zach Teitler, Douglas A. Torrance, Castelnuovo-Mumford regularity and arithmetic Cohen-Macaulayness of complete bipartite subspace arrangements, JPAA 219 (2015), Issue 6, 2134--2138
  17. Weronika Buczyńska, Jarosław Buczyński, Zach Teitler, Waring decompositions of monomials, J. Algebra 378 (2013), 45--57.
  18. Zach Teitler, Topological criteria for schlichtness, Proceedings of the Edinburgh Mathematical Society (Series 2) 56 (2013), no. 2, 637--640.
  19. Javier Elizondo, Paulo Lima-Filho, Frank Sottile, Zach Teitler, Arithmetic toric varieties, Math. Nach. 287 (2014), Issue 2-3, 216--241
  20. Luis García-Puente, Nickolas Hein, Christopher J. Hillar, Abraham Martín del Campo, James Ruffo, Frank Sottile, Zach Teitler, The Secant Conjecture in the real Schubert calculus, Exp. Math. 21 (2012), no. 3, 252--265
  21. Thomas Bauer, Cristiano Bocci, Susan Cooper, Sandra Di Rocco, Marcin Dumnicki, Brian Harbourne, Kelly Jabbusch, Andreas Leopold Knutsen, Alex Küronya, Rick Miranda, Joaquim Roé, Hal Schenck, Tomasz Szemberg, Zach Teitler, Recent developments and open problems in linear series. In "Contributions to Algebraic Geometry", IMPANGA Lecture Notes, August 2012
  22. Susan Cooper, Brian Harbourne, Zach Teitler, Combinatorial bounds on Hilbert functions of fat points in projective space, J. Pure Appl. Algebra 215 (2011), no. 9, 2165--2179
  23. Nero Budur, Mircea Mustață, Zach Teitler, The Monodromy Conjecture for hyperplane arrangements, Geom. Dedicata 153 (2011), 131--137
  24. Christopher Hillar, Luis García-Puente, Abraham Martín del Campo, James Ruffo, Zach Teitler, Stephen L. Johnson, Frank Sottile, Experimentation at the Frontiers of Reality in Schubert Calculus, Contemp. Math. 517 (2010), 365--380
  25. J.M. Landsberg, Zach Teitler, On the ranks and border ranks of symmetric tensors, Found. Comput. Math. 10 (2010), no. 3, 339--366
  26. Zach Teitler, Bounding symbolic powers via asymptotic multiplier ideals, Ann. Acad. Pedagog. Crac. Stud. Math. 8 (2009), 67--77
  27. Ulrich Derenthal, Michael Joyce, Zach Teitler, The nef cone volume of generalized Del Pezzo surfaces, Algebra & Number Theory 2 (2008), no. 2, 157--182
  28. Zach Teitler, A note on Mustață's computation of multiplier ideals of hyperplane arrangements, Proc. Amer. Math. Soc. 136 (2008), no. 5, 1575--1579
  29. Zach Teitler, On the intersection of the curves through a set of points in P^2, J. Pure Appl. Algebra 209 (2007), no. 2, 571--581
  30. Zach Teitler, Multiplier ideals of general line arrangements in C^3, Comm. Alg. 35 (2007), no. 6, 1902--1913

Unpublished

  1. Zach Teitler, Geometric lower bounds for generalized ranks

Software

  1. MultiplierIdeals - a Macaulay2 package for computing multiplier ideals of special ideals including monomial ideals, monomial curves, and generic determinantal ideals.
  2. ApolarIdeal - a Macaulay2 package for computing apolar ideals
  3. CombinatorialIteration - a Macaulay2 package providing iterators for several common combinatorial structures

Secant experimental project.