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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. Gallery of selected works.


Publications

  1. Zach Teitler, Sufficient conditions for Strassen's additivity conjecture
    submitted
    arXiv:1604.07691 [math.AG]
  2. 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]
  3. 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]
  4. 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]
  5. 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]
  6. Zach Teitler, Geometric lower bounds for generalized ranks
    arXiv:1406.5145 [math.AG]
  7. 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]
  8. 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]
  9. 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]
  10. 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]
  11. Zach Teitler, Software for multiplier ideals, JSAG 7 (2015), no. 1, 1--8
    Published paper
    arXiv:1305.4435 [math.AG]
  12. Zach Teitler, Alex 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]
  13. 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]
  14. Weronika Buczyńska, Jarosław Buczyński, Zach Teitler, Waring decompositions of monomials, J. Algebra 378 (2013), 45--57.
    Published paper
    arXiv:1201.2922 [math.AG]
  15. 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]
  16. 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]
  17. 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]
  18. 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]
  19. 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]
  20. 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]
  21. 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]
  22. 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]
  23. 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]
  24. 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]
  25. 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]
  26. 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]
  27. 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]

Secant experimental project.


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

Selected Presentations

  1. Colloquium for my application for tenure and promotion, titled "Recent advances in Waring rank and apolarity" presented at Boise State on September 5, 2013
  2. Talk on "Direct sum decomposability of polynomials" presented at Interactions between Commutative Algebra and Algebraic Geometry II, Tulane, New Orleans, September 28-29, 2013
  3. Poster on "Three Directions in Waring Ranks and Apolarity" presented at Robfest, May 17, 2013
  4. Colloquium talk on "Ranks of polynomials" presented at University of Idaho on March 27, 2014
  5. Pi Day Hap-Pi-ness: Irrationally Cool Facts About Pi talk for Boise State Math Club on Friday, March 13, 2015

Expository writing

  1. Some time ago, I began work on a short expository set of notes on Chern classes in algebraic geometry, particularly in the context of enumerative problems. The notes are not polished. Some day I hope to finish them; in the meantime, I have uploaded a draft, in PDF format (21 pages): An informal introduction to computing with Chern classes (May 31, 2014).
  2. Some expository notes based on talks I gave in the TAMU Several Complex Variables seminar in February 2008 on multiplier ideals, aimed at relating resolution of singularities to the problem of simplifying integrals. (July 16, 2008: v0.2. Numerous minor improvements.)

Here is a modest collection of links to pages which in turn link to interesting sources for algebraic geometry.

zteitler@boisestate.edu


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