Research

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

I study algebraic geometry with actual polynomials, especially Waring rank.

My dissertation was titled “Multiplier Ideals of Line Arrangements”. I computed the multiplier ideals of general arrangements of lines through the origin in $\mathbb{C}^3$, 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

2020
[31]
Garritt Johns and Zach Teitler, An improved upper bound for the Waring rank of the determinant, J. Comm. Alg.
 
[30]
Brian Harbourne, Juan Migliore, Uwe Nagel, and Zach Teitler, Unexpected hypersurfaces and where to find them, Michigan Math. J.
 
[29]
Mats Boij, Zach Teitler, A bound for the Waring rank of the determinant via syzygies, Linear Alg. Appl.
2018
[28]
Jarosław Buczyński, Kangjin Han, Massimiliano Mella, and Zach Teitler, On the locus of points of high rank, European J. Math.
2017
[27]
Theodosios Douvropoulos, Joachim Jelisiejew, Bernt Ivar Utstøl Nødland, Zach Teitler, The Hilbert scheme of $11$ points in $\mathbb{A}^3$ is irreducible, in: Combinatorial Algebraic Geometry
2016
[26]
Nathan Ilten and Zach Teitler, Product ranks of the $3 \times 3$ determinant and permanent, Canad. Math. Bull.
 
[25]
Erik Holmes, Paul Plummer, Jeremy Siegert, and Zach Teitler, Maximum Waring ranks of monomials and sums of coprime monomials, Comm. Alg.
 
[24]
Jarosław Buczyński and Zach Teitler, Some examples of forms of high rank, Collect. Math.
 
[23]
Kent M. Neuerburg and Zach Teitler, Decompositions of ideals of minors meeting a submatrix, Comm. Alg.
 
[22]
Harm Derksen and Zach Teitler, Lower bound for ranks of invariant forms, JPAA
2015
[21]
Zach Teitler, Sufficient conditions for Strassen’s additivity conjecture, Illinois J. Math.
 
[20]
Zach Teitler, Software for multiplier ideals, JSAG
 
[19]
Zach Teitler and Alexander Woo, Power sum decompositions of defining equations of reflection arrangements, J. Alg. Comb.
 
[18]
Nickolas Hein, Christopher J. Hillar, Abraham Martín del Campo, Frank Sottile, Zach Teitler, The monotone secant conjecture in the real Schubert calculus, Exp. Math.
 
[17]
Grigoriy Blekherman, Zach Teitler, On maximum, typical, and generic ranks, Math. Ann.
 
[16]
Zach Teitler and Douglas A. Torrance, Castelnuovo-Mumford regularity and arithmetic Cohen-Macaulayness of complete bipartite subspace arrangements, JPAA
 
[15]
Weronika Buczyńska, Jarosław Buczyński, Johannes Kleppe, and Zach Teitler, Apolarity and direct sum decomposability of polynomials, Michigan Math. J.
2014
[14]
Javier Elizondo, Paulo Lima-Filho, Frank Sottile, and Zach Teitler, Arithmetic toric varieties, Math. Nach.
2013
[13]
Zach Teitler, Topological criteria for schlichtness, Proc. Edinb. Math. Soc. (2)
 
[12]
Weronika Buczyńska, Jarosław Buczyński, and Zach Teitler, Waring decompositions of monomials, J. Algebra
2012
[11]
Luis García-Puente, Nickolas Hein, Christopher J. Hillar, Abraham Martín del Campo, James Ruffo, Frank Sottile, and Zach Teitler, The Secant Conjecture in the real Schubert calculus, Experimental Math.
 
[10]
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, Contributions to Algebraic Geometry, IMPANGA Lecture Notes
2011
[9]
Nero Budur, Mircea Mustață, and Zach Teitler, The Monodromy Conjecture for hyperplane arrangements, Geom. Dedicata
 
[8]
Susan Cooper, Brian Harbourne, and Zach Teitler, Combinatorial bounds on Hilbert functions of fat points in projective space, JPAA
2010
[7]
Christopher Hillar, Luis García-Puente, Abraham Martín del Campo, James Ruffo, Zach Teitler, Stephen L. Johnson, and Frank Sottile, Experimentation at the Frontiers of Reality in Schubert Calculus, Contemp. Math.
 
[6]
J. M. Landsberg and Zach Teitler, On the ranks and border ranks of tensors and symmetric tensors, Found. Comput. Math.
2009
[5]
Zach Teitler, Bounding symbolic powers via asymptotic multiplier ideals, Ann. Univ. Pedagog. Crac. Stud. Math.
2008
[4]
Ulrich Derenthal, Michael Joyce, and Zach Teitler, The nef cone volume of generalized Del Pezzo surfaces, Algebra & Number Theory
 
[3]
Zach Teitler, A note on Mustață’s computation of multiplier ideals of hyperplane arrangements, PAMS
2007
[2]
Zachariah C. Teitler, Multiplier ideals of general line arrangements in $\mathbb{C}^3$, Comm. Alg.
 
[1]
Zachariah C. Teitler, On the intersection of the curves through a set of points in $\mathbb{P}^2$, JPAA

Unpublished

  1. Geometric lower bounds for generalized ranks

Software

  1. MultiplierIdeals.m2

  2. ApolarIdeal.m2

  3. CombinatorialIteration.m2