Nathan Ryan is a Professor of Mathematics at Bucknell University.
MATH 216: Statistics I and MATH 208: Mathematical Explorations
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.
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:
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
presented at American Medical Informatics Association conference
- 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
- analyzing publicly available parole data to see what demographic
features influece parole decisions
- Student collaborators: Junjie Jiang '19
- poster presented at Kalman
- 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 to appear 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 submitted to Journal of Open Source Software, repository on
Ongoing projects include
- analyzing Department of Corrections data to understand what factors
influence parole decision (partnered with Professor Mir in Computer
Science and Professor Massaro in Geography),
- 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,
- modeling the change of color use in Hollywood blockbuster films over
the last 30 years (partnered with Professor Faden in Film and Media
Selected Papers († indicates undergraduate
- Ryan, Nathan C.; Scherr, Zachary; Sirolli, Nicolás;
Stephanie. "Congruences satisfied by eta-quotients." To appear in Proc. Amer. Math. Soc.. ArXiv Version.
- Armendáriz†, David; Colman†, Owen; Coloma†, Nicolás; Ghitza, Alexandru; Ryan, Nathan C.; Terán†, Darío. "Analytic evaluation of
Hecke eigenvalues for classical modular forms" ArXiv Version.
- Barquero-Sanchez, Adrian; Mantilla-Soler, Guillermo;
Ryan, Nathan C. "Theta series and number fields: theorems and experiments" To appear Ramanujan J. ArXiv Version.
- 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.
- 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.
- Ryan, Nathan C. "Coding and cryptography: number theory applied to three love stories." (Spanish) Publ. Mat. Urug. 15 (2016), 123–139.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Ryan, Nathan C.; Tornaría, Gonzalo. "A Böcherer-type conjecture for paramodular forms." Int. J. Number Theory 7 (2011), no. 5, 1395–1411. ArXiv Version.
- 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
- 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
- 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.
- Bach, Eric; Ryan, Nathan C. "Efficient verification of Tunnell's criterion." Japan J. Indust. Appl. Math. 24 (2007), no. 3, 229–239. Personal version
- Pomerance, Carl; Ryan, Nathan C. "Maximal height of divisors of $x^n-1$." Illinois J. Math. 51 (2007), no. 2, 597–604. Personal version
- Ryan, Nathan C. "Satake Parameters of Siegel Modular Forms", Dartmouth College Thesis (2005).