Nathan C. Ryan

Nathan Ryan is a Professor of Mathematics at Bucknell University and an affiliate faculty member in the Latin America Studies program.

Teaching

• Two sections of Math 211: Multivariable Calculus

A few years ago I developed a class in Mathematical Modelling for Biologists, based on a class taught by Dorothy Wallace. The notes for this course have recently been turned into a book, co-authored with Dorothy, available from World Scientific Press.

Projects

• I am trained as a computational number theorist and am most interested in computations involving modular forms and L-functions.
• I am an editor of the L-functions and Modular Database (LMFDB).
• I am an editor for Frontiers for Young Minds, a journal reviewed and read by young scientists. Write me a note if you might be interested in contributing.
• I am an affiliate of the Institute for the Quantitative Study of Inclusion, Diversity, and Equity.
• With students I work on interdisciplinary projects in applied data science.
• I have been awarded Fulbright Scholar Grants to Uruguay (2009), Ecuador (2017) and Costa Rica (2022). If you have any questions about the program, particularly if you're a mathematician, please don't hesitate to write.

Undergraduate research projects

If you are a Bucknell student interested in doing undergraduate research with me, please drop me a line. Usually I work with students with a strong computer science/programming background, but would be happy to work with any motivated student.

Recent projects include:

• analyzing patient flow through a hospital system using Markov models (partnered with Geisinger in Danville, PA)
  • Student Collaborators: Maria Cioffi '16, Naba Mukhtar '17
  • paper in American Medical Informatics proceedings
• predicting onset of septic shock for septic patients (partnered with Geisinger in Danville, PA)
  • Student Collaborators: Alex Robinson '17, Murph '18
  • poster presented at American Medical Informatics Association conference 2017
• determining how equitably distributed access to health care is in Colorado (partnered with Farley Health Center in Colorado)
  • Student Collaborators: Yash Bhutwala '17, Jordan Kovacs '20, Alex Robinson '17, Trung Tran '19
  • poster presented at the North American Primary Care Research Group conference 2016
• analyzing publicly available parole data to see what demographic features influece parole decisions
• Student collaborators: Junjie Jiang '19
• poster presented at Kalman symposium 2019.
• applying statistical techniques and data visualization techniques to eye-tracking data to study the films of Jacques Tati (partnered with Professor Faden in Film and Media Studies and Professor Mitchel in Psychology)
• Student collaborators: Alexander Murph '18
• paper published in Projections: The Journal for Movies and Mind
• applying various tools in computer vision to analyze the use of color in film (partnered with Professor Faden in Film and Media Studies)
• Student collaborators: Yida Chen '22
• paper published in Journal of Open Source Software, repository on GitHub
• analyzing data from the Pennsylvania Department of Corrections related to how incarcerated people are securitized (partnered with Professor Massaro in Geography and Professor Mir in Computer Science
• Student collaborators: Swarup Dhar '22preprints available here, here, and here.

Ongoing projects include

• comparing the performance of ArcGIS routing tools and a genetic algorithm implemented in Python for the routing of school buses in the Lewsiburg Area School District (partnered with LASD and Janine Glathar, GIS specialist)
• modeling the change of color use in Hollywood blockbuster films over the last 30 years (partnered with Professor Faden in Film and Media Studies)

Honors Theses

• Verifying Harder's Conjecture for Classical and Siegel Modular Forms by David Sulon '12
• Random Matrix Theory and the Attraction of Zeros of L-Functions From the Central Point by Katherin Harris '15

Selected Papers (^† indicates undergraduate co-author)

1. Berg, Jennifer; Ryan, Nathan C.; Young, Matthew P. "Vanishing of quartic and sextic twists of L-functions." Research in Number Theory (2024): 10(1):20.
2. Barquero-Sanchez, Adrian; Collado-Valverde, Gabriel; Ryan, Nathan C.; Salas-Jimenez, Eduardo; Sirolli, Nicolás; Villegas-Morales, Jean Carlos. "Efficient computation of the overpartition function and applications." Journal of Mathematical Analysis and Applications (2023): 127472.
3. Massaro, Vanessa; Dhar, Swarup; Mir, Darakhshan; Ryan, Nathan C. "Carceral algorithms and the history of control: An analysis of the Pennsylvania additive classification tool." Big Data & Society 9.1 (2022): 20539517221094002
4. Ryan, Nathan C.; Scherr, Zachary; Sirolli, Nicolás; Treneer, Stephanie. "Congruences satisfied by eta-quotients." Proc. Amer. Math. Soc. 149, no. 3 (2021): 1039-1051. ArXiv Version.
5. Armendáriz^†, David; Colman^†, Owen; Coloma^†, Nicolás; Ghitza, Alexandru; Ryan, Nathan C.; Terán^†, Darío. "Analytic evaluation of Hecke eigenvalues for classical modular forms" ArXiv Version.
6. Barquero-Sanchez, Adrian; Mantilla-Soler, Guillermo; Ryan, Nathan C. "Theta series and number fields: theorems and experiments" Ramanujan J. (2021): 1-18 ArXiv Version.
7. Colman^†, Owen; Ghitza, Alexandru; Ryan, Nathan C. "Analytic evaluation of Hecke eigenvalues for Siegel modular forms of degree two". Proceedings of the Thirteenth Algorithmic Number Theory Symposium, 207–220, Open Book Ser., 2, Math. Sci. Publ., Berkeley, CA, 2019. ArXiv Version.
8. Farmer, David W.; Pitale, Ameya; Ryan, Nathan C.; Schmidt, Ralf. "Analytic L Functions: definitions, theorems and connections". Bull. Amer. Math. Soc. (N.S.) 56 (2019), no. 2, 261–280.. ArXiv Version.
9. Ryan, Nathan C. "Coding and cryptography: number theory applied to three love stories." (Spanish) Publ. Mat. Urug. 15 (2016), 123–139.
10. Ryan, Nathan C.; Sirolli, Nicolás; Skoruppa, Nils-Peter; Tornaría, Gonzalo. "Computing Jacobi forms." LMS J. Comput. Math. 19 (2016), suppl. A, 205–219. ArXiv Version.
11. Ryan, Nathan C.; Tornaría, Gonzalo. "Formulas for central values of twisted spin L-functions attached to paramodular forms. With an appendix by Ralf Schmidt". Math. Comp. 85 (2016), no. 298, 907–929. ArXiv Version.
12. Ryan, Nathan C.; Tornaría, Gonzalo; Voight, John. "Nonvanishing of twists of L-functions attached to Hilbert modular forms." LMS J. Comput. Math. 17 (2014), suppl. A, 330–348. ArXiv Version.
13. Farmer, David W.; Ryan, Nathan C. "Evaluating L-functions with few known coefficients." LMS J. Comput. Math. 17 (2014), no. 1, 245–258. ArXiv Version.
14. Farmer, David W.; Pitale, Ameya; Ryan, Nathan C.; Schmidt, Ralf. "Survey article: Characterizations of the Saito-Kurokawa lifting." Rocky Mountain J. Math. 43 (2013), no. 6, 1747–1757. ArXiv Version.
15. Ghitza, Alexandru; Ryan, Nathan C.; Sulon^†, David. "Computations of vector-valued Siegel modular forms." J. Number Theory 133 (2013), no. 11, 3 921–3940. ArXiv Version.
16. Ryan, Nathan C.; Skoruppa, Nils-Peter; Strömberg, Fredrik. "Numerical computation of a certain Dirichlet series attached to Siegel modular forms of degree two." Math. Comp. 81 (2012), no. 280, 2361–2376. ArXiv Version.
17. Farmer, David W.; Ryan, Nathan C.; Schmidt, Ralf. "Testing the functional equation of a high-degree Euler product." Pacific J. Math. 253 (2011), no. 2, 349–366. ArXiv Version.
18. Ryan, Nathan C.; Tornaría, Gonzalo. "A Böcherer-type conjecture for paramodular forms." Int. J. Number Theory 7 (2011), no. 5, 1395–1411. ArXiv Version.
19. Ryan, Nathan C.; Ward^†, Bryan C.; Ward^†, Ryan. "Some conjectures on the maximal height of divisors of $x^n-1$." Involve 3 (2010), no. 4, 451–457. ArXiv Version.
20. Poor, Cris; Ryan, Nathan C.; Yuen, David S. "Lifting puzzles in degree four." Bull. Aust. Math. Soc. 80 (2009), no. 1, 65–82. Personal version
21. Ryan, Nathan C.; Shemanske, Thomas R. "Inverting the Satake map for $Sp_n$ and applications to Hecke operators." Ramanujan J. 17 (2008), no. 2, 219–244. Personal version.
22. Bach, Eric; Ryan, Nathan C. "Efficient verification of Tunnell's criterion." Japan J. Indust. Appl. Math. 24 (2007), no. 3, 229–239. Personal version
23. Pomerance, Carl; Ryan, Nathan C. "Maximal height of divisors of $x^n-1$." Illinois J. Math. 51 (2007), no. 2, 597–604. Personal version
24. Ryan, Nathan C. "Satake Parameters of Siegel Modular Forms", Dartmouth College Thesis (2005).