BYU COMPUTATIONAL NUMBER THEORY RESEARCH GROUP DAVID CARDON, DARRIN DOUD, PAUL JENKINS, AND PACE NIELSEN

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Pace Nielsen, Mathematics

Evaluation of Academic Objectives

In the years 2013-2014 we held a weekly seminar in which every supported student gave presentations at least once (but usually twice or more) per semester. This gave the students opportunities to learn and develop presentations skills, which will help them later in their careers. It also gave them opportunities to work together in a tight-knit group setting. This learning was augmented by regular, one-on-one weekly meetings with their advisors. Many of the students wrote professional research papers published in peer-reviewed journals, presented their research at conferences, and many won prestigious university and even national awards.

A list of supported students, along with important products developed under the support of the MEG grant, are listed in the next section. The final section describes expenditures.

List of Supported Students and Products

  • Joseph Adams: January 2013-May 2014, Advisor: Darrin Doud
    • Spoke at the 2014 CPMS Student Research Conference.
    • Accepted into the BYU Mathematics PhD program, 2014.
  • Wil Cocke: January 2013-May 2014, Advisor: Darrin Doud
    • Gave a presentation at the 2014 Automorphic Forms Workshop, Moab, UT.
    • Attended a workshop on \The Cohomology of Arithmetic Groups” in Chicago, in 2013.
    • Attended the UNCG Summer School in Computational Number Theory in May, 2014.
    • Attended the following three conferences: NSF-CBMS Regional Conference in the Mathematical Sciences on Combinatorial Zeta and L-Functions (2014), MAA Spring Sectional Meeting (2014), and Curves and Automorphic Forms Workshop, ASU (2014).
    • Received the NSF Graduate Research Fellowship award in 2014.
    • Accepted to the University of Wisconsin Mathematics PhD program, 2014. 
  • Kevin Childers: January 2013-December 2014, Advisor: Darrin Doud
    • Won the Orson Pratt Prize, 2013.
    • Submitted paper: Kevin Childers and Darrin Doud, Proof of a conjecture of Wong concerning octahedral Galois representations with prime power conductor, 2014.
    • Spoke at the 2013 CPMS Student Research Conference.
    • Spoke at the 2014 CPMS Student Research Conference.
    • Accepted into the BYU Mathematics masters program, 2013. 
  • Samuel J. Dittmer: January 2013-May 2014, Advisor: Pace Nielsen
    • Spoke at the 2013 CPMS Student Research Conference.
    • Gave a presentation at the 2014 Automorphic Forms Workshop, Moab, UT.
    • Honorable mention on the 2013 Putnam competition, placed 49 nationally.
    • Attended the Texas A&M REU in 2013.
    • Accepted to the Arizona Winter School in 2014.
    • Published paper: Samuel J. Dittmer, Spoof odd perfect numbers, Math. Comp. 83:2575- 2582, 2014.
    • Published paper: Samuel J. Dittmer, Dinesh Khurana, and Pace P. Nielsen, On a question of Hartwig and Luh. Bull. Austral. Math. Soc. 89:271-278, 2014.
    • Paper in preparation: Alexander J. Diesl, Samuel J. Dittmer, and Pace P. Nielsen, Idem- potent lifting properties which do not lift to ring extensions, 2014.
    • Won the Orson Pratt Prize, 2014.
    • Honorable mention for the NSF Graduate Fellowship, 2014.
    • Accepted to the UCLA Mathematics PhD program, 2014. 
  • Nathan Green: January 2013-August 2013, Advisor: Paul Jenkins
    • Attended 2013 Arizona Winter School, funded by conference.
    • Submitted paper: N. Green and P. Jenkins, Integral traces of weak Maass forms of genus zero odd prime level, 2014.
    • Graduated from BYU with a masters degree.
    • Accepted to Texas A&M Mathematics PhD program, 2013.
  • Andrew Haddock: January 2013-April 2014, Advisor: Paul Jenkins
    • Published paper: A. Haddock and P. Jenkins, Zeros of weakly holomorphic modular forms of level 4, International Journal of Number Theory 10(2):455-470, 2014.
    • Received an individual BYU ORCA grant in 2014.
    • Gave a presentation at the 2013 Automorphic Forms Workshop, University College Dublin, Ireland.
    • Spoke at the 2014 CPMS Student Research Conference.
    • Attended the 2014 Automorphic Forms Workshop, Moab, UT.
    • Received the National Health Service Corps scholarship for dental school at the University of Minnesota in 2014. 
  • Benjamin Herrera: BS December 2014, Advisor: Paul Jenkins
    • Spoke at the 2014 CPMS Student Research Conference.
    • Attended the 2014 Automorphic Forms Workshop, Moab, UT. 
  • Chris Hettinger: January 2013-August 2014, Advisor: Paul Jenkins
    • Spoke at the 2013 CPMS Student Research Conference.
    • Spoke at the 2014 CPMS Student Research Conference.
    • Provisional patent led on an algorithm he developed.
    • Graduated from BYU with a masters degree.
    • Accepted to the BYU Mathematics PhD program, 2014.
  • Tyler Owens: January 2013-December 2014, Advisors: Darrin Doud and Pace Nielsen
    • Spoke at the 2013 CPMS Student Research Conference.
    • Spoke at the 2014 CPMS Student Research Conference, and won his section.
    • Submitted paper: Tyler Owens, A covering system with minimum modulus 42, 2014.
    • Graduated from BYU with a masters degree in 2014.
  • Kyle Pratt: January 2013-June 2014, Advisor: Paul Jenkins
    • Published paper: P. Jenkins and K. Pratt, Interlacing of zeros of weakly holomorphic modular forms, Proceedings of the American Mathematical Society, Series B 1, 63-77, 2014.
    • Published paper: J. Andrade, S. Miller, K. Pratt, and M. Trinh, Special sets of primes in function fields, INTEGERS 14, #A18, 2014.
    • Submitted paper: P. Jenkins and K. Pratt, Coecient bounds for level 2 cusp forms and modular functions, 2014.
    • Received an individual BYU ORCA grant in 2014.
    • Received the NSF Graduate Research Fellowship award in 2014.
    • Gave presentations at the 2013 Automorphic Forms Workshop, University College Dublin, Ireland; and at the 2013 Maine/Quebec Number Theory Conference, University of Maine.
    • Attended 2014 Automorphic Forms Workshop, Moab, UT.
    • Attended 2014 Arizona Winter School.
    • Attended 2013 REU at Williams College.
    • Accepted to the University of Illinois at Urbana-Champaign Mathematics PhD program, 2014. 
  • DJ Thornton: January 2013-December 2014, Advisor: Paul Jenkins
    • Published paper: P. Jenkins and DJ Thornton, Congruences for coecients of modular functions, The Ramanujan Journal, to appear, 2015.
    • Participated in the 2013 NSA Director’s Summer Program.
    • Gave presentations at the 2013 Automorphic Forms Workshop, University College Dublin, Ireland; and at the 2014 Automorphic Forms Workshop, Moab, UT.
    • Spoke at the 2014 CPMS Student Research Conference.
    • Currently in the MS program at BYU.

Descriptions of Budget Spending

Here are some of the major items on which the students were supported financially. 

  • In many of the semesters, we bought textbooks from which the students studied and gave presentations in our weekly seminar.
  • We supported students who attended the Arizona Winter School. This is a week long conference focused on involving graduate (and some undergraduate) students in current research in number theory. This support included Nathan Green in 2013, and Wil Cocke, Samuel Dittmer, and Kyle Pratt in 2014. Some students were reimbursed. 
  • We sent three students to the 2013 Automorphic Forms Workshop at the University College Dublin, in Ireland; namely Andrew Haddock, Kyle Pratt, and DJ Thornton. The students were partially reimbursed by the conference. 
  • We sent six students to the 2014 Automorphic Forms Workshop in Moab, UT. 
  • Other assorted trips for individual students to professional conferences.