Paul Jenkins, Mathematics
In 2017 and 2018, the following students participated in the BYU Computational Number Theory research group under my direction and produced the following deliverables.
1. Hankun Ko, BYU PhD student in mathematics (PhD 2019 expected)
a. Spoke at 2017 Student Research Conference
b. Spoke at 2018 Student Research Conference
c. Attended 31st Automorphic Forms Workshop at East Tennessee State University, March 2017
d. Attended 32nd Automorphic Forms Workshop at Tufts University, March 2018
2. Daniel Adams, BYU MS student in mathematics (MS 2017)
a. Spoke at 2017 Student Research Conference
b. Presented at 31st Automorphic Forms Workshop at East Tennessee State University, March 2017
c. Thesis: Spaces of weakly holomorphic modular forms of level 52
3. Kit Vander Wilt, BYU MS student in mathematics (MS 2017)
a. Spoke at 2017 Student Research Conference
b. Presented at 31st Automorphic Forms Workshop at East Tennessee State University, March 2017
c. Thesis: Weakly holomorphic modular forms in level 64
4. Grant Molnar, BYU MS student in mathematics (MS 2018)
a. Spoke at 2017 Student Research Conference
b. Presented at 31st Automorphic Forms Workshop at East Tennessee State University, March 2017
c. Presented at 32nd Automorphic Forms Workshop at Tufts University, March 2018
d. Presentation (speed talk) at Modular Forms are Everywhere conference, Max Planck Institute for Mathematics, Bonn, Germany, May 24, 2017
e. Presentation at Building Bridges: 4th EU/US Workshop on Automorphic Forms and Related Topics, Alfréd Rényi Institute of Mathematics, Budapest, Hungary, July 17, 2018
f. 2018 NSF Graduate Research Fellowship Honorable Mention
g. P. Jenkins and G. Molnar, Zagier duality for level p weakly holomorphic modular forms, The Ramanujan Journal (2018), doi: 10.1007/s11139-018-0009-8
h. M. Griffin, P. Jenkins, and G. Molnar, The arithmetic of modular grids, in preparation
5. Eric Moss, BYU undergraduate and MS student in mathematics (BS 2017, MS 2018)
a. Spoke at 2017 Student Research Conference
b. Spoke at 2018 Student Research Conference
c. Presented at 31st Automorphic Forms Workshop at East Tennessee State University, March 2017
d. Presented at 32nd Automorphic Forms Workshop at Tufts University, March 2018
e. Presentation (speed talk) at Modular Forms are Everywhere conference, Max Planck Institute for Mathematics, Bonn, Germany, May 26, 2017
f. Presentation at Building Bridges: 4th EU/US Workshop on Automorphic Forms and Related Topics, Alfréd Rényi Institute of Mathematics, Budapest, Hungary, July 18, 2018
g. P. Jenkins, R. Keck, and E. Moss, Congruences for coefficients of level 2 modular functions with poles at 0, Archiv der Mathematik 111 (2018) no. 4, 369-378
6. Ryan Keck, BYU undergraduate and MS student in mathematics (BS 2018, MS 2020 expected)
a. Spoke at 2017 Student Research Conference
b. Spoke at 2018 Student Research Conference
c. Presented at 31st Automorphic Forms Workshop at East Tennessee State University, March 2017
d. Attended 32nd Automorphic Forms Workshop at Tufts University, March 2018
e. P. Jenkins, R. Keck, and E. Moss, Congruences for coefficients of level 2 modular functions with poles at 0, Archiv der Mathematik 111 (2018) no. 4, 369-378
7. Merrill Warnick, BYU undergraduate in mathematics (BS 2018)
a. Spoke at 2017 Student Research Conference
b. Presented at 31st Automorphic Forms Workshop at East Tennessee State University, March 2017
c. V. Iba, P. Jenkins, and M. Warnick, Divisibility properties of coefficients of modular functions in genus zero levels, Integers, to appear d. BYU honors thesis, fall 2018
8. Victoria Iba, BYU undergraduate in mathematics (BS 2017)
a. Spoke at 2017 Student Research Conference
b. Presented at 31st Automorphic Forms Workshop at East Tennessee State University, March 2017
c. V. Iba, P. Jenkins, and M. Warnick, Divisibility properties of coefficients of modular functions in genus zero levels, Integers, to appear
9. Miriam Beazer, BYU undergraduate in mathematics
In addition to the three publications and paper in preparation noted above, the paper Weakly holomorphic modular forms in prime power levels of genus zero, which I wrote with DJ Thornton, a BYU masters student, was published in the journal Integers in 2018, and the paper Integral traces of weak Maass forms of genus zero odd prime level, which I wrote with Nathan Green, a BYU masters student, was published in the Ramanujan Journal in 2017. Additionally, most of these students participated in the joint paper written by the BYU Computational Number Theory Group, Spoof odd perfect numbers, which should be submitted for publication in 2019.
I believe that the BYU Computational Number Theory Research Group has been very successful. Many students have written published papers and given talks at conferences, sometimes as the only undergraduates presenting. Students from the group have gone on to graduate school at Boston College, Dartmouth, and BYU, and taken jobs at NSA and Goldman Sachs. The mentoring environment clearly contributed to this success, with a well-attended weekly seminar and opportunities for students to learn from each other.
The budget from the grant was largely spent funding the students’ travel to attend and present at multiple mathematics conferences. A small amount of the funding helped contribute to pizza or snacks for the group occasionally at the weekly seminar meetings.