Research papers:

• "Dynamical convergence of polynomials to products of power maps and the exponential," with Devin Becker and Lorelei Koss, New York Journal of Mathematics, 29 (2023) 441-466. https://nyjm.albany.edu/j/2023/29-19.html 

• “Bounded remainder sets for rotations on higher dimensional adelic tori,” with Akshat Das and Alan Haynes, Moscow Journal of Combinatorics and Number Theory, 10 (2020) no. 2, 111-120. https://doi.org/10.2140/moscow.2021.10.111 

• “Natural extensions for p-adic beta shifts and other scaling maps,” Indagationes Mathematicae, 30 (2019) no. 6, 1099-1108. https://doi.org/10.1016/j.indag.2019.08.005

• "Bounded remainder sets for rotations on the adelic torus," with Alan Haynes and Henna Koivusalo. Proceedings of the AMS, 147 (2019) no. 12, 5105-5115. https://www.ams.org/journals/proc/2019-147-12/S0002-9939-2019-14636-0/S0002-9939-2019-14636-0.pdf

• “Relating singularly perturbed rational maps to families of entire maps,” with Lorelei Koss, in Dynamical Systems and Random Processes, Contemporary Mathematics, 736 (2019) 49-68. https://www.ams.org/books/conm/736/14834

• "Rational families converging to a family of exponential maps," with Jane Hawkins and Lorelei Koss. Journal of Fractal Geometry, 6 (2019) no. 1, 89-108. https://www.ems-ph.org/journals/show_pdf.php?issn=2308-1309&vol=6&iss=1&rank=4

• "Everywhere divergence of the one-sided ergodic Hilbert transform for circle rotations by Liouville numbers,” with David Constantine. New York Journal of Mathematics. 23 (2017), 273-294. http://nyjm.albany.edu/j/2017/23-14.html

• "Haar measures and Hausdorff dimensions of p-adic Julia sets." Ergodic Theory, Dynamical Systems, and the Continuing Influence of John C. Oxtoby, Contemporary Mathematics. 678 (2016), 187-196. https://www.ams.org/books/conm/678/13647

• "Approximations for p-adic transitive isometries." Topology Proceedings. 46 Oct. 2015, 323-338. http://topology.auburn.edu/tp/reprints/v46/tp46023.pdf

• "Singular p-adic transformations for Bernoulli product measures." New York Journal of Mathematics. 20 (2014), 799-812. http://nyjm.albany.edu/j/2014/20-40.html

• "Orbit equivalence of p-adic transformations and their Iterates." Monatshefte für Mathematik 175 (2014), no. 2, 249-276. https://link.springer.com/article/10.1007/s00605-014-0645-z

Under Review:

• “Geometric limits of Julia sets in two complex variables," with Scott Kaschner.

Thesis:

• "Ergodic Theory of p-adic Transformations," Ph.D. Thesis, University of North Carolina at Chapel Hill, May 2013. Carolina Digital Repository 

Undergraduate Work:

The following papers contain research that I participated in as an undergraduate. The first paper was completed as part of an REU at Oregon State University. The last two papers are on research completed while I worked in Kerry Kuehn's physics lab at Wisconsin Lutheran College.

• Furno, Joanna and Patrick Waters. “Investigations Regarding Partitions and Multipartitions.” Proceedings of the Research Experiences for Undergraduates Program in Mathematics, Oregon State University, Summer 2007. REU Proceedings.

• Furno, Joanna and Kerry Kuehn. “Tidal Pattern Instabilities on Multi-moon Planets.” Icarus, Vol. 189, Issue 1, Jul. 2007, 246-255. https://www.sciencedirect.com/science/article/abs/pii/S0019103507000516

• Kuehn, Kerry, Jonathan Polfer, Joanna Furno, and Nathan Finke. “Apparatus for Real-time Acoustic Imaging of Rayliegh-Bénard Convection.” Review of Scientific Instruments, Vol. 78, Issue 11, Nov. 2007. https://aip.scitation.org/doi/abs/10.1063/1.2804133