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Research Interests Jeffrey Meier

Broadly, I am interested in knot theory, knotted surfaces, and the topology of 3-manifolds and 4-manifolds. In particular, I have a great interest in trisections of 4-manifolds; 4-dimensional knot theory, including fibered ribbon 2-knots, knotted Klein bottles and projective planes, surgery operations, and bridge trisections; various aspects of knot concordance, including doubly slice knots, fibered ribbon knots, cabled slice knots, and applications of knot homology theories; and Dehn surgery, especially exceptional surgery and Seifert fibered surgery. For more information, see my Research Statement.

Publications

  1. Generalized square knots and homotopy 4-spheres [arXiv] with Alexander Zupan
  2. Bridge trisections in rational surfaces [arXiv] with Peter Lambert-Cole
  3. Doubly pointed trisection diagrams and surgery on 2-knots [arXiv] with David Gay
  4. Trisections and spun 4-manifolds [arXiv]
    Mathematical Research Letters 25(5) (2018), 1497 – 1524
  5. Bridge trisections of knotted surfaces in 4-manifolds [arXiv] with Alexander Zupan
    Proceedings of the National Academy of Sciences 115(43) (2018), 10880-10886
  6. Characterizing Dehn surgery on links via trisections [arXiv] with Alexander Zupan
    Procedings of the National Academy of Science 115(43) (2018), 10887-10893
  7. Bridge trisections of knotted surfaces in S4 [arXiv] with Alexander Zupan
    Transactions of the AMS, Vol. 369 (2017), 7343-7386
  8. Genus two trisections are standard [arXiv] with Alexander Zupan
    Geometry & Topology 21 (2017), 1583-1630
  9. A note on cabled slice knots and reducible surgeries [arXiv]
    Michigan Mathematics Journal Vol. 66, Issue 2 (2017), 269-276
  10. Classifying trisections and the Generalized Property R Conjecture [arXiv] with Alexander Zupan and Trenton Schirmer -- Proceedings of the AMS, Vol. 144(11) (2016), 4983-4997
  11. Doubly slice knots with low crossing number [arXiv] with Charles Livingston
    New York Journal of Mathematics, Vol. 21 (2015), 1007-1026
  12. Fibered ribbon disks [arXiv] with Kyle Larson
    Journal of Knot Theory and Its Ramifications, Vol. 24 (2015), 1550066, pp. 22
  13. Distinguishing topologically and smoothly doubly slice knots [arXiv]
    Journal of Topology 8 (2015), 315-351
  14. Small Seifert fibered surgery on hyperbolic pretzel knots [arXiv]
    Algebraic & Geometric Topology 14 (2014), 439-487
  15. Isolation-by-distance and outbreeding depression are sufficient to drive parapatric speciation in the absence of environmental influences with René Doursat, Rich Drewes, and Guy Hoelzer
    PLoS Computational Biology 4(7) (2008), 11 pp.

Videos and Slides

Here are some videos and slides from talks I've given.

Invited Talks

Below is a selection of invited talks I've given, along with links to some of the corresponding videos and slides.