Jennifer Johnson-Leung
Professor
University of Idaho
University of Idaho
Contact 
Jennifer Johnson-Leung
Department of Mathematics and Statistical Science
875 Perimeter Drive, MS 1103
University of Idaho
Moscow ID 83844-1103
USA
jenfns-AT-uidaho-DOT-edu
Office Hours:
303 Brink Hall
By appointment
Other Links
Google Scholar Profile
Github Profile
LinkedIn Profile
Curriculum Vitae
Here is my CV as a pdf.
References available upon request.
Research
Research Publications and Preprints
- Johnson-Leung, J., McGlade, F., Negrini, I., Pollack, A., & Roy, M. (2024) The quaternionic Maass Spezialschar on split SO(8)-arXiv preprint arXiv:2401.15277 (Submitted)
(Show/Hide Abstract)The classical Maass Spezialschar is a Hecke-stable subspace of the level one holomorphic Siegel modular forms of genus two, i.e., on Sp(4), cut out by certain linear relations between the Fourier coefficients. It is a theorem of Andrianov, Maass, and Zagier, that the classical Maass Spezialschar is exactly equal to the space of Saito-Kurokawa lifts. We study an analogous space of quaternionic modular forms on split SO(8), and prove the analogue of the Andrianov-Maass-Zagier theorem. Our main tool for proving this theorem is the development of a theory of a Fourier-Jacobi coefficient of quaternionic modular forms on orthogonal groups. - Johnson-Leung, J. and Rupert, N. (2024) An explicit theta lift to Siegel Modular Forms (to appear in Women in Numbers 6)
(Show/Hide Abstract)Let $E/L$ be a real quadratic extension of number fields. We construct an explicit map from an irreducible cuspidal automorphic representation of $\mathrm{GL}(2,E)$ which contains a Hilbert modular form with $\Gamma_0$ level to an irreducible automorphic representation of $\mathrm{GL}(4,L)$ which contains a Siegel paramodular form and exhibit local data which produces a paramodular invariant vector for the local theta lift at every finite place, except when the local extension has wild ramification. - Johnson-Leung, J., Parker, J., & Roberts, B. (2023) The paramodular Hecke algebra- arXiv preprint arXiv:2310.13179 (Accepted to Research in Number Theory)
(Show/Hide Abstract)We give a presentation via generators and relations of the local graded paramodular Hecke algebra of prime level. In particular, we prove that the paramodular Hecke algebra is isomorphic to the quotient of the free $\mathbb{Z}$-algebra generated by four non-commuting variables by an ideal generated by seven relations. Using this description, we derive rationality results at the level of characters and give a characterization of the center of the Hecke algebra. Underlying our results are explicit formulas for the product of any generator with any double coset. - Seamon, E., Ridenhour, B.J., Miller, C.R., Johnson-Leung, J. (2023) Spatial Modeling of Sociodemographic Risk for COVID-19 Mortality (preprint-submitted)
(Show/Hide Abstract)In early 2020, the Coronavirus Disease 19 (COVID-19) rapidly spread across the United States, exhibiting significant geographic variability. While several studies have examined the predictive relationships of differing factors on COVID-19 deaths, few have looked at spatiotemporal variation at refined geographic scales. The objective of this analysis is to examine spatiotemporal variation of COVID-19 deaths in association with socioeconomic, health, demographic, and political factors, using regionalized multivariate regression as well as nationwide county-level geographically weighted random forest (GWRF) models. Analyses were performed on data from three sepearate timeframes: pandemic onset until May 2021, May 2021 through November 2021, and December 2021 until April 2022.Regionalized regression results across three time windows suggest that existing measures of social vulnerability for disaster preparedness (SVI) are associated with a higher degree of mortality from COVID-19. In comparison, GWRF models provide a more robust evaluation of feature importance and prediction, exposing the importance of local features, such as obesity, which is obscured by regional delineation. Overall, GWRF results indicate a more nuanced modeling strategy is useful for capturing the diverse spatial and temporal nature of the COVID-19 pandemic. - Sarathchandra, D. and Johnson-Leung, J. (2024) Influence of Political Ideology and Media on Vaccination Intention in the Early Stages of the COVID-19 Pandemic in the United States COVID 2024, 4(5), 658-671; (Show/Hide Abstract)
As a pharmaceutical intervention, vaccines remain a major public health strategy for mitigating the effects of COVID-19. Yet, vaccine uptake has been affected by various cognitive and cultural barriers. We examine how a selected set of barriers (i.e., knowledge, concern, media, peer influence, and demographics) shaped COVID-19 vaccination intention in the early phase of the pandemic (Fall 2020). Using a survey conducted in three US states (Idaho, Texas, and Vermont) just prior to the roll out of the first vaccines against COVID-19, we find that COVID-19 concern was the primary driver of vaccination intention. Concern was shaped mainly by two factors: political ideology and media sources. Yet, ideology and media were much more important in affecting concern for those who leaned politically conservative, as opposed to those who leaned liberal or remained moderate. The results from our Structural Equation Models affirm that the information politically conservative respondents were receiving reinforced the effects of their ideology, leading to a greater reduction in their concern. We discuss the potential implications of these findings for future pandemic preparedness.
- Moxley, T.A., Johnson-Leung, J., Seamon, E., Williams, C., & Ridenhour, B.J., (2024) Application of Elastic Net Regression for Modeling COVID-19 Sociodemographic Risk Factors (PLoS ONE 19(1): e0297065).
(Show/Hide Abstract)Objectives: COVID-19 has been at the forefront of global concern since its emergence in December of 2019. Determining the social factors that drive case incidence is paramount to mitigating disease spread. We gathered data from the Social Vulnerability Index (SVI) along with Democratic voting percentage to attempt to understand which county-level sociodemographic metrics had a significant correlation with case rate for COVID-19.
Methods: We used elastic net regression due to issues with variable collinearity and model overfitting. Our modelling framework included using the ten Health and Human Services regions as submodels for the two time periods 22 March 2020 to 15 June 2021 (prior to the Delta time period) and 15 June 2021 to 1 November 2021 (the Delta time period).
Results: Statistically, elastic net improved prediction when compared to multiple regression, as almost every HHS model consistently had a lower root mean square error (RMSE) and satisfactory R 2 coefficients. These analyses show that the percentage of minorities, disabled individuals, individuals living in group quarters, and individuals who voted Democratic correlated significantly with COVID-19 attack rate as determined by Variable Importance Plots (VIPs).
Conclusions: The percentage of minorities per county correlated positively with cases in the earlier time period and negatively in the later time period, which complements previous research. In contrast, higher percentages of disabled individuals per county correlated negatively in the earlier time period. Counties with an above average percentage of group quarters experienced a high attack rate early which then diminished in significance after the primary vaccine rollout. Higher Democratic voting consistently correlated negatively with cases, coinciding with previous findings regarding a partisan divide in COVID-19 cases at the county level. Our findings can assist policymakers in distributing resources to more vulnerable counties in future pandemics based on SVI.
- Johnson-Leung, J., Roberts, B., & Schmidt, R. (2023) Stable Klingen Vectors and Paramodular Newforms Springer Lecture Notes in Mathematics, Volume 2342.
(Show/Hide Abstract)We introduce the family of stable Klingen congruence subgroups of $\mathrm{GSp}(4)$. We use these subgroups to study both local paramodular vectors and Siegel modular forms of degree 2 with paramodular level. In the first part, when $F$ is a nonarchimedean local field of characteristic zero and $(\pi,V)$ is an irreducible, admissible representation of $\mathrm{GSp}(4,F)$ with trivial central character, we establish a basic connection between the subspaces $V_s(n)$ of $V$ fixed by the stable Klingen congruence subgroups and the spaces of paramodular vectors in V and derive a fundamental partition of the set of paramodular representations into two classes. We determine the spaces $V_s(n)$ for all $(\pi,V)$ and $n$. We relate the stable Klingen vectors in $V$ to the two paramodular Hecke eigenvalues of $\pi$ by introducing two stable Klingen Hecke operators and one level lowering operator. In contrast to the paramodular case, these three new operators are given by simple upper block formulas. We prove further results about stable Klingen vectors in $V$ especially when $\pi$ is generic. In the second part we apply these local results to a Siegel modular newform $F$ of degree 2 with paramodular level $N$ that is an eigenform of the two paramodular Hecke operators at all primes $p$. We present new formulas relating the Hecke eigenvalues of $F$ at $p$ to the Fourier coefficients $a(S)$ of $F$ for $p^2\mid N$. We verify that these formulas hold for a large family of examples and indicate how to use our formulas to generally compute Hecke eigenvalues at $p$ from Fourier coefficients of $F$ for $p^2\mid N$. Finally, for $p^2\mid N$ we express the formal power series in $p^{-s}$ with coefficients given by the radial Fourier coefficients $a(p^tS)$, $t\geq0$, as an explicit rational function in $p^{-s}$ with denominator $L_p(s,F)^{-1}$, where $L_p(s,F)$ is the spin $L$-factor of $F$ at $p$. - Ridenhour, B.J., Sarathchandra, D., Seamon, E., Brown, H., Leung, F-Y., Johnson-Leon, M, Megheib, M., Miller, C.R., Johnson-Leung, J. (2022) Effects of trust, risk perception, and health behavior on COVID-19 disease burden: Evidence from a multi-state US survey. PLoS ONE 17(5): e0268302.
(Show/Hide Abstract)Early public health strategies to prevent the spread of COVID-19 in the United States relied on non-pharmaceutical interventions (NPIs) as vaccines and therapeutic treatments were not yet available. Implementation of NPIs, primarily social distancing and mask wearing, varied widely between communities within the US due to variable government mandates, as well as differences in attitudes and opinions. To understand the interplay of trust, risk perception, behavioral intention, and disease burden, we developed a survey instrument to study attitudes concerning COVID-19 and pandemic behavioral change in three states: Idaho, Texas, and Vermont. We designed our survey (n = 1034) to detect whether these relationships were significantly different in rural populations. The best fitting structural equation models show that trust indirectly affects protective pandemic behaviors via health and economic risk perception. We explore two different variations of this social cognitive model: the first assumes behavioral intention affects future disease burden while the second assumes that observed disease burden affects behavioral intention. In our models we include several exogenous variables to control for demographic and geographic effects. Notably, political ideology is the only exogenous variable which significantly affects all aspects of the social cognitive model (trust, risk perception, and behavioral intention). While there is a direct negative effect associated with rurality on disease burden, likely due to the protective effect of low population density in the early pandemic waves, we found a marginally significant, positive, indirect effect of rurality on disease burden via decreased trust (p = 0.095). This trust deficit creates additional vulnerabilities to COVID-19 in rural communities which also have reduced healthcare capacity. Increasing trust by methods such as in-group messaging could potentially remove some of the disparities inferred by our models and increase NPI effectiveness. - Johnson-Leung, J., & Roberts,
B. (2017) Fourier Coefficients for Twists of
Siegel Paramodular Forms. J. Ramanujuan Math Soc. 32 (2) pp 101-119. Expanded version on Arxiv.
(Show/Hide Abstract)In this paper, we calculate the Fourier coefficients of the paramodular twist of a Siegel modular form of paramodular level $N$ by a nontrivial quadratic Dirichlet character mod $p$ for $p$ a prime not dividing $N$. As an application, these formulas can be used to verify the nonvanishing of the twist for particular examples. We also deduce that the twists of Maass forms are identically zero. - Johnson-Leung, J., & Roberts, B. (2017) Twisting of Siegel Paramodular Forms. Int. J. Number Theory, 13 (7) pp. 1755-1854.
(Show/Hide Abstract)
Let $S_k(\Gamma^{\mathrm{para}}(N))$ be the space of Siegel paramodular forms of level $N$ and weight $k$. Let $p\nmid N$ and let $\chi$ be a nontrivial quadratic Dirichlet character mod $p$. Based on our previous work, we define a linear twisting map $\mathcal{T}_\chi:S_k(\Gamma^{\mathrm{para}}(N))\rightarrow S_k(\Gamma^{\mathrm{para}}(Np^4))$. We calculate an explicit expression for this twist and give the commutation relations of this map with the Hecke operators and Atkin-Lehner involution for primes $\ell\neq p$.
- Yopp, D., Ely, R., and Johnson-Leung, J. (2015) Generic
Example Proving Criteria for All. (pdf) 35 3, 8–13.
For the Learning of Mathematics.
(Show/Hide Abstract)Our goal is to provide criteria for determining if an exam- ple in an argument is being used as a generic example. We write in response to Leron and Zaslavsky’s (2013) discus- sion of generic examples, which we agree with in some ways and disagree with in others. -
Johnson-Leung, J., & Roberts, B. (2014) Twisting of paramodular vectors.
International
Journal of Number Theory,
10 1043–1065 (doi:
10.1142/S1793042114500146).
(Show/Hide Abstract)Let $F$ be a non-archimedean local field of characteristic zero, let $(\pi,V)$ be an irreducible, admissible representation of $\mathrm{GSp}(4,F)$ with trivial central character, and let $\chi$ be a quadratic character of $F^\times$ with conductor $c(\chi)>1$. We define a twisting operator $T_\chi$ from paramodular vectors for $\pi$ of level $n$ to paramodular vectors for $\chi \otimes \pi$ of level $\max(n+2c(\chi),4c(\chi))$, and prove that this operator has properties analogous to the well-known $\mathrm{GL}(2)$ twisting operator. -
Johnson-Leung, J. (2013) The local equivariant Tamagawa number conjecture for almost abelian extensions.
In Women in Numbers 2: Research Directions
in Number Theory, Contemporary Mathematics, 606 1–27.
(Show/Hide Abstract)We prove the local equivariant Tamagawa number conjecture for the motive of an abelian extension of an imaginary quadratic field with the action of the Galois group ring for all split primes $p\neq 2, 3$ at all integer values $s < 0$. -
Johnson-Leung, J., & Roberts, B. (2012) Siegel modular forms of degree two attached to Hilbert modular forms.
Journal of Number Theory, 132 ,543–564.
(Show/Hide Abstract)Let $E/\mathbb{Q}$ be a real quadratic field and $\pi_0$ a cuspidal, irreducible, automorphic representation of $\mathrm{GL}(2,\mathbb{A}_E)$ with trivial central character and infinity type $(2,2n+2)$ for some non-negative integer $n$. We show that there exists a Siegel paramodular newform $F: \mathfrak H_2 \to \mathbb C$ with weight, level, Hecke eigenvalues, epsilon factor and $L$-function determined explicitly by $\pi_0$. We tabulate these invariants in terms of those of $\pi_0$ for every prime $p$ of $\mathbb{Q}$. - H. Grundman, J. Johnson-Leung, K. Lauter, A. Salerno,
B. Viray, and E. Wittenborn. (2011) Embeddings of
Quartic CM fields and Intersection theory on the
Hilbert Modular Surface, in WIN--Women in Numbers:
Research Directions in Number Theory, Fields Institute
Communications Series, Volume 60, 35–60.
(Show/Hide Abstract)Bruinier and Yang conjectured a formula for an intersection number on the arithmetic Hilbert modular surface, $CM(K).T_m$, where $CM(K)$ is the zero-cycle of points corresponding to abelian surfaces with CM by a primitive quartic CM field $K$, and $T_m$ is the Hirzebruch-Zagier divisors parameterizing products of elliptic curves with an m-isogeny between them. In this paper, we examine fields not covered by Yang's proof of the conjecture. We give numerical evidence to support the conjecture and point to some interesting anomalies. We compare the conjecture to both the denominators of Igusa class polynomials and the number of solutions to the embedding problem stated by Goren and Lauter. - Johnson-Leung, J., & Kings, G. (2011) On the equivariant
main conjecture for imaginary quadratic fields,
J. reine angew. Math. 653
75–114.
(Show/Hide Abstract)In this paper we first prove the main conjecture for imaginary quadratic fields for all prime numbers $p$, improving earlier results by Rubin. From this we deduce the equivariant main conjecture in the case that a certain $\mu$-invariant vanishes. For prime numbers $p\nmid 6$ which split in $K$, this is a theorem by a result of Gillard.
Other work
- Fox, S.J., Johnson, K., Owirodu, B., Johnson-Leung, J., Elizondo, M., Walkes, D., Ancel Meyers, L. (2022) COVID-19 Risk Assessment for Public Events.(pdf). University of Texas COVID-19 Modeling Consortium.
(Show/Hide Abstract)We describe a risk assessment framework to support event planning during COVID-19 waves. The method was developed in partnership with public health officials in Austin, Texas. - Buow, I., Ozman, E., Johnson-Leung, J., Newtown, R. (Editors) (2018) Women in Numbers Europe II: Contributions to Number Theory and Arithmetic Geometry. Association for Women in Mathematics Series (AWMS, volume 11) Springer Cham.
(Show/Hide Abstract)Inspired by the September 2016 conference of the same name, this second volume highlights recent research in a wide range of topics in contemporary number theory and arithmetic geometry. Research reports from projects started at the conference, expository papers describing ongoing research, and contributed papers from women number theorists outside the conference make up this diverse volume. Topics cover a broad range of topics such as arithmetic dynamics, failure of local-global principles, geometry in positive characteristics, and heights of algebraic integers. The use of tools from algebra, analysis and geometry, as well as computational methods exemplifies the wealth of techniques available to modern researchers in number theory. Exploring connections between different branches of mathematics and combining different points of view, these papers continue the tradition of supporting and highlighting the contributions of women number theorists at a variety of career stages. Perfect for students and researchers interested in the field, this volume provides an easily accessible introduction and has the potential to inspire future work. - Johnson-Leung, J. (2017) Hyperelliptic Threshold Noise: A Mathematician's Perspective. Essay accompanying the Visualizing Science Exhibit.
- Johnson-Leung, J. (2005) Artin $L$-functions for abelian
extensions of imaginary quadratic fields. PhD Thesis,
California Institute of
Technology. 1–69.
(Show/Hide Abstract)Let $F$ be an abelian extension of an imaginary quadratic field $K$ with Galois group $G$. We form the Galois-equivariant $L$-function of the motive $M=h^0(\mathrm{Spec}(F))(j)$ where the Tate twists $j$ are negative integers. The leading term in Taylor expansion at $s=0$ decomposes over the group algebra $\mathbb{Q}[G]$ into a product of Artin $L$-functions indexed by the characters of $G$. We construct a motivic element $\xi$ via the Eisenstein symbol and relate the $L$-value to periods of $\xi$ via regulator maps. Working toward the equivariant Tamagawa number conjecture, we prove that the $L$-value gives a basis in étale cohomology which coincides with the basis given by the $p$-adic $L$-function according to the main conjecture of Iwasawa theory.
Funding
- Co-PI: Fundamental Principles of Cybersecurity (2023-2026)
Schweitzer Engineering Laboratory, $865,000 - Co-Director: Supplement for COVID-19 modeling (2020–2021)
NIH COBRE Supplement Project, CMCI, $492,598 - PI: “Gear Up!” (2017)
Micron Foundation Gift, $5,000 - Co-PI: Making Mathematical Reasoning Explicit (2011–2016)
NSF Award #1050397, $4,996,102 - PI: “Special Values of L-functions and Motivic Elements for Abelian Surfaces with Complex Multiplication.” (2010–2012)
NSA Young Investigator's grant, $30,000 - PI: “Special Values of L-functions of CM fields” (2008–2009)
University of Idaho Seed Grant, $9,000
Teaching and Advising
PhD Students
Undergraduate Students
I have mentored over a dozen undergraduate students in research and independent study. The students listed below received Undergraduate Research Fellowships. If you are interested in doing research with me or need a letter of recommendation, please come to my office hours or send me an email to set up an appointment.- Katie Thiessen (BS 2025, Hill, Co-advised with James Nagler)
- Trevor Griffin, (BS 2021, Hill)
- Kirk Bonney (BS 2020, Hill)
- Beau Horenberger (BS 2019, SURF)
Teaching
I teach a wide range of mathematics courses at the graduate and undergraduate level. In Fall 2025, I will be teaching an inquiry-based writing-intensive course called Proof via Number Theory as well as one of the core courses in our graduate algebra sequence, Groups and Fields I. Several of my courses are available through the Engineering Outreach platform. Students may access those videos through the EO Portal.I use canvas for my course web pages.