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Assistant Professor Mathematics zupan@unl.edu 308 Avery Hall

My previous page, http://www.math.unl.edu/~azupan2/, will no longer be active as of July 1, 2020. Be sure to change your browser to remove the ~ from my URL.

Contact Information

Mailing Address:
308 Avery Hall
Department of Mathematics
University of Nebraska-Lincoln
Lincoln, NE 68588-0130

FAX: 402-472-8466

CV

Teaching

Spring 2019: M107 – Calculus II, M872 – Topology II

Fall 2018: M106 – Calculus I, M871 – Topology I

Spring 2018: M872 – Topology II

Spring 2017: M314 – Linear Algebra, M990 – Topics in Topology

Spring 2016: M208 – Multivariable Calculus, M221 – Differential Equations

Fall 2015: M208 – Multivariable Calculus, M314 – Linear Algebra

Research

My research is in geometric topology, low-dimensional topology, and knot theory.

Below are some of my publications.

Preprints:

  • (with Jeffrey Meier) Generalized square knots and homotopy 4-spheres, (2019), submitted. [arXiv]
  • (with Rebecca Sorsen) The Kauffman bracket expansion of a generalized crossing, (2019), submitted. [PDF]

Publications:

  • The Powell conjecture and reducing sphere complexes, J. London Math. Soc. (2) (2019), first published online. [arXiv]
  • (with Jeffrey Meier) Bridge trisections for knotted surfaces in 4-manifolds, Proc. Nat. Acad. Sci. 115 (2018), no. 43, 10880-10886. [arXiv] [journal]
  • (with Jeffrey Meier) Characterizing Dehn surgeries on links via trisections, Proc. Nat. Acad. Sci. 115 (2018), no. 43, 10887-10893. [arXiv] [journal]
  • (with Derek Davies) Natural properties of the trunk of a knot, J. Knot Theory and Ramifications 26 (2017), no. 12, 1750080, 9 pp. [arXiv] [journal]
  • (with Jeffrey Meier) Genus-two trisections are standard, Geom. Topol. 21 (2017), no. 3, 1583-1630. [arXiv] [journal]
  • (with Jeffrey Meier) Bridge trisections of knotted surfaces in S^4, Trans. Amer. Math. Soc. 369 (2017), no. 10, 7343-7386. [arXiv] [journal]
  • (with Jessica Purcell) Independence of volume and genus g bridge numbers, Proc. Amer. Math. Soc. 145 (2017), no. 4, 1805-1818. [arXiv] [journal]
  • (with Jeffrey Meier and Trent Schirmer) Classification of trisections and the Generalized Property R Conjecture, Proc. Amer. Math. Soc. 144 (2016), no. 11, 4983-4997. [arXiv] [journal]
  • (with Samuel Taylor) Products of Farey graphs are totally geodesic in the pants graph, J. Topol. Anal., Online ready. [arXiv] [journal]
  • (with B. Kang, A. Kronaeur, P. Luitel, D. Medici, and S. A. Taylor) New Examples of Brunnian theta graphs, Involve 9 (2016), no. 2, 287-311. [arXiv] [journal]
  • Uniqueness of higher genus bridge surfaces for torus knots, Math. Proc. Cambridge Philos. Soc. 159 (2015), no. 1, 79-88. [arXiv] [journal]
  • (with Ryan Blair) Knots with compressible thin levels, Alg. Geom. Top. 15 (2015), no. 3, 1691-1715. [arXiv] [journal]
  • (with Sean Bowman and Scott Taylor) Bridge spectra of twisted torus knots, Int. Math. Res. Notices (2015), no. 16, 7336-7356. [arXiv] [journal]
  • Bridge spectra of iterated torus knots, Comm. Anal. Geom. 22 (2014), no. 5, 931-963. [arXiv] [journal]
  • Infinite cardinalities in the Hausdorff metric geometry, Involve 7 (2014), 585-593. [journal]
  • Bridge and pants complexities of knots, J. London Math. Soc. (2) 87 (2013), 43-68. [arXiv] [journal]
  • A lower bound on the width of satellite knots, Top. Proc. 40 (2012), 179-188. [arXiv] [journal]
  • Properties of knots preserved by cabling, Comm. Anal. Geom. 19 (2011), no. 3, 541-562. [arXiv] [journal]
  • Unexpected local minima in the width complexes for knots, Alg. Geom. Top. 11 (2011), no. 2, 1097-1106. [arXiv] [journal]
  • (with C. Blackburn, K. Lund, S. Schlicker, and P. Sigmon) A missing prime configuration in the Hausdorff Metric Geometry, J. Geom. 92 (2009), no. 1-2, 28-59. [journal]

Outreach

I am currently on the organizing committee for the Nebraska Conference for Undergraduate Women in Mathematics. I also organize the Great Plains Alliance program at UNL.

Links of Interest

I have a finite Erdös-Bacon number.