Publications

Time for Math. To appear in the December 2024 issue of the Notices of the American Mathematical Society.
Seeds for Building Community. With C. Hsu. Nov 2022 issue of the Notices of the American Mathematical Society.
The Seattle Universal Math Museum: Transforming Perceptions of Math. Oct/Nov 2022 issue of MAA Focus.
Illustrating Mathematics. A review of a book featuring creations from a semester-long program on Illustrating Mathematics.
Improv-ing a Mathematician's Professional Skills. An article I wrote for MAA FOCUS, the Mathematical Association of America's newsmagazine, about the impact of improv training on my professional development.
Moving Ahead in Your Research. An article I wrote for the Early Career section of the Notices of the American Mathematical Society.
Creativity Counts. Math Buffet column in the Girls' Angle Bulletin. Volume 15 (2021), no. 1, 12--16 and cover image.
A blogpost I wrote for SAMSI describing the the first NSF/NIH "Innovation Lab" about a new interdisciplinary program in biomedical data science.

Algebraicity of Spin L-functions for GSp₆. With G. Rosso and S. Shah. 60 pages. arXiv preprint.

Constructing vector-valued automorphic forms on unitary groups. With T. L. Browning, P. Čoupek, C. Frechette, S. Hong, S. Y. Lee, and D. Marcil. 32 pages. arXiv preprint.

Archimedean zeta integrals for unitary groups. With Z. Liu. Journal für die reine und angewandte Mathematik (Crelles Journal) 2024 (2024), No. 813, 103--132.

Automorphic forms on unitary groups. In Automorphic Forms Beyond GL_2: Lectures from the 2022 Arizona Winter School. Mathematical Surveys and Monographs 279, American Mathematical Society (2024), 1--58.

Entire theta operators at unramified primes. With E. Mantovan. International Mathematics Research Notices (2022), No. 21, 16405-16463.

p-adic families of automorphic forms in the mu-ordinary setting. With E. Mantovan. American Journal of Mathematics, 143 (2021), No. 1, 1-52.

An Introduction to Eisenstein Measures. Journal de Théorie des Nombres de Bordeaux. Vol. 33 (2021), No. 3.1, 779-808.

Differential operators mod p: analytic continuation and consequences. With M. Flander, A. Ghitza, E. Mantovan, and A. McAndrew. Algebra & Number Theory. Vol. 15 (2021), No. 6, 1469-1504.

p-adic L-functions for unitary groups. With M. Harris, J.-S. Li, and C. Skinner. Forum of Mathematics, Pi, 8 (2020), E9, 160 pages.

Applications of nonarchimedean developments to archimedean nonvanishing results for twisted L-functions. Math. Res. Lett. 27 (2020), No. 4, 973-1002.

A Gallery of Gaussian Periods. With S. Garcia. Proceedings of Bridges 2020: Mathematics, Art, Music, Architecture, Education, Culture. Carolyn Yackel, Robert Bosch, Eve Torrence, and Kristóf Fenyvesi, eds., Tessellations Publishing (2020), 243–248.

Gaussian Periods

Bootstrapping estimates of stability for clusters, observations, and model selection. H. Yu, B. Chapman, A. Di Florio, E. Eischen, D. Gotz, M. Jacob, and R. Hageman Blair. Computational Statistics. Vol. 34 (2019), Issue 1, 349-372.

bootcluster

Differential operators and families of automorphic forms on unitary groups of arbitrary signature. With J. Fintzen, E. Mantovan, and I. Varma. Doc. Math. 23 (2018), 445-495.

p-adic L-Functions of Finite Slope Forms on Unitary Groups and Eisenstein Series. With X. Wan. J. Inst. Math. Jussieu. Vol. 15 (2016), 471-510.

Differential operators, pullbacks, and families of automorphic forms. Annales Mathematiques du Quebec. Vol. 40. Issue 1 (2016), 55-82.

p-adic q-expansion principles on unitary Shimura varieties. With A. Caraiani, J. Fintzen, E. Mantovan, and I. Varma. Directions in Number Theory: Proceedings of the 2014 WIN3 Workshop. Springer International Publishing (2016), 197-243.

A p-adic Eisenstein Measure for Unitary Groups. J. Reine Angew. Math. 699 (2015), 111–142.

A p-adic Eisenstein measure for vector-weight automorphic Forms. Algebra & Number Theory. Vol. 8 (2014), No. 10, 2433-2469.

p-adic differential operators on automorphic forms on unitary groups. Annales de l’Institut Fourier. Volume 62, No. 1 (2012), 177-243.
This paper is based on my dissertation:

p-adic Differential Operators on Automorphic Forms and Applications. ProQuest LLC, Ann Arbor, MI. (2009), 130 pages.

Decomposition of almost complete tripartite graphs into two isomorphic factors of fixed diameter. Discrete Mathematics. 306 (2006), 745-761.

Patterns, linesums, and symmetry. With C. Johnson, K. Lange, and D. Stanford. Linear Algebra and its Applications. 357 (2002), 273-289.

Articles for Broader Audiences

Articles for Mathematicians

Current:

Associate Editor, Research in Number Theory

Associate Editor, Essential Number Theory

Co-editor, Directions in Number Theory: Proceedings of the 2014 WIN3 Workshop. Springer International Publishing (2016).

My primary area of research is number theory. Many of the articles below concern automorphic forms and L-functions, which link seemingly disparate data in number theory and beyond. I especially focus on algebraic and p-adic aspects.

Editorial Work

App on Mac App Store

The Gaussian Periods app is now available for Apple Computers on the Mac App Store! Everyone from novices to experts can use this app, whether purely for fun or for exploratory analysis.

Ellen Eischen