Articles for Mathematicians

Current:

Associate Editor, Research in Number Theory

Associate Editor, Essential Number Theory

Previous:

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

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- 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 GSp*With G. Rosso and S. Shah. 60 pages. arXiv preprint._{6}.*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.*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.*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.

Associated app: Gaussian Periods (now available on the Mac App Store!)

Associated R package: bootcluster

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