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
- Mats Boij, Zach Teitler, A bound for the Waring rank of the determinant via syzygies, Linear Alg. Appl. 587 (2020), 195--214
- Published paper
- arXiv:1908.08896 [math.AG]
- Brian Harbourne, Juan Migliore, Uwe Nagel, Zach Teitler, Unexpected hypersurfaces and where to find them, Michigan Math. J., to appear
- arXiv:1805.10626 [math.AG]
- 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
- Published paper
- arXiv:1703.02829 [math.AG]
- 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
- arxiv:1701.03089 [math.AG]
- Zach Teitler, Sufficient conditions for Strassen's additivity conjecture, Illinois J. Math. 59 (2015), no. 4, 1071--1085
- Published paper
- arXiv:1604.07691 [math.AG]
- Jarosław Buczyński, Zach Teitler, Some examples of forms of high rank, Collect. Math. 67 (2016), no. 3, 431--441
- Published paper
- arXiv:1503.08253 [math.AG]
- Nathan Ilten, Zach Teitler, Product ranks of the $3 \times 3$ determinant and permanent, Canad. Math. Bull. 59 (2016), no. 2, 311--319
- Published paper
- arXiv:1503.00822 [math.AG]
- Harm Derksen, Zach Teitler, Lower bound for ranks of invariant forms, JPAA 219 (2015), no. 12, 5429--5441
- Published paper
- arXiv:1409.0061 [math.AG]
- Kent M. Neuerburg, Zach Teitler, Decompositions of ideals of minors meeting a submatrix, Comm. Alg. 44 (2016), no. 4, 1809--1820
- Published paper
- arXiv:1406.6426 [math.AC]
- 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
- (paper version of extended abstract presented in MEGA 2011)
- Published paper
- arXiv:1109.3436 [math.AG]
- Grigoriy Blekherman, Zach Teitler, On maximum, typical, and generic ranks, Math. Ann. 362 (2015), no. 3--4, 1021--1031
- Published paper
- arXiv:1402.2371 [math.AG]
- 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
- Published paper
- arXiv:1309.7834 [math.AG]
- Weronika Buczyńska, Jarosław Buczyński, Johannes Kleppe, Zach Teitler, Apolarity and direct sum decomposability of polynomials, Michigan Math. J. 64 (2015), no. 4, 675--719.
- Published paper
- arXiv:1307.3314 [math.AG]
- Zach Teitler, Software for multiplier ideals, JSAG 7 (2015), no. 1, 1--8
- Published paper
- arXiv:1305.4435 [math.AG]
- Zach Teitler, Alexander Woo, Power sum decompositions of defining equations of reflection arrangements, J. Alg. Comb. 41 (2015), Issue 2, 365--383
- Published paper
- arXiv:1304.7202 [math.AG]
- Zach Teitler, Douglas A. Torrance, Castelnuovo-Mumford regularity and arithmetic Cohen-Macaulayness of complete bipartite subspace arrangements, JPAA 219 (2015), Issue 6, 2134--2138
- Published paper
- arXiv:1209.2075 [math.AG]
- Weronika Buczyńska, Jarosław Buczyński, Zach Teitler, Waring decompositions of monomials, J. Algebra 378 (2013), 45--57.
- Published paper
- arXiv:1201.2922 [math.AG]
- Zach Teitler, Topological criteria for schlichtness, Proceedings of the Edinburgh Mathematical Society (Series 2) 56 (2013), no. 2, 637--640.
- Published paper
- arXiv:1004.3947 [math.CV]
- Javier Elizondo, Paulo Lima-Filho, Frank Sottile, Zach Teitler, Arithmetic toric varieties, Math. Nach. 287 (2014), Issue 2-3, 216--241
- Published paper
- arXiv:1003.5141 [math.AG]
- 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
- Published paper
- arXiv:1010.0665 [math.AG]
- 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
- Published paper
- arXiv:1101.4363 [math.AG]
- 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
- Published paper
- arXiv:0912.1915 [math.AG]
- Nero Budur, Mircea Mustață, Zach Teitler, The Monodromy Conjecture for hyperplane arrangements, Geom. Dedicata 153 (2011), 131--137
- Published paper
- arXiv:0906.1991 [math.AG]
- 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
- Published paper
- arXiv:0906.2497 [math.AG]
- J.M. Landsberg, Zach Teitler, On the ranks and border ranks of symmetric tensors, Found. Comput. Math. 10 (2010), no. 3, 339--366
- Published paper
- arXiv:0901.0487 [math.AG]
- Zach Teitler, Bounding symbolic powers via asymptotic multiplier ideals, Ann. Acad. Pedagog. Crac. Stud. Math. 8 (2009), 67--77
- Published paper
- arXiv:0907.4045 [math.AG]
- Ulrich Derenthal, Michael Joyce, Zach Teitler, The nef cone volume of generalized Del Pezzo surfaces, Algebra & Number Theory 2 (2008), no. 2, 157--182
- Published paper
- arXiv:math/0703202 [math.AG]
- Zach Teitler, A note on Mustață's computation of multiplier ideals of hyperplane arrangements, Proc. Amer. Math. Soc. 136 (2008), no. 5, 1575--1579
- Published paper
- arXiv:math/0610303 [math.AG]
- 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
- Published paper
- arXiv:math/0508307 [math.AG]
- Zach Teitler, Multiplier ideals of general line arrangements in C^3, Comm. Alg. 35 (2007), no. 6, 1902--1913
- Published paper
- arXiv:math/0508308 [math.AG]
Unpublished
- Zach Teitler, Geometric lower bounds for generalized ranks
- arXiv:1406.5145 [math.AG]
Software
- MultiplierIdeals - a Macaulay2 package for computing multiplier ideals of special ideals including monomial ideals, monomial curves, and generic determinantal ideals.
- ApolarIdeal - a Macaulay2 package for computing apolar ideals
- CombinatorialIteration - a Macaulay2 package providing iterators for several common combinatorial structures