Research and Thesis Students
Here is a list of my current and former research and thesis students since 2014 (at Yale and Amherst) and the work they completed under my supervision.

Yale University (2010-2014)

• Sam Kimport,Yale University, Ph.D. student 2010-2015
  (Post-graduation position: Stanford University, Lecturer in Mathematics.)

• Ph.D. Thesis: “Quantum modular forms, mock modular forms, and partial theta functions,” Yale University, 2015.

• Graded dimensions of principal subspaces and modular Andrews-Gordon series, (by K. Bringmann, C. Calinescu, A. Folsom, and S. Kimport). Communications in Contemporary Mathematics 16 no. 4 (2014), 1350050 [20 pages].

• Mock modular forms and singular combinatorial series, (by A. Folsom and S. Kimport). Acta Arithmetica 159.3 (2013), 257-297.

• Quantum modular forms and singular combinatorial series with distinct roots of unity, (by A. Folsom, M-J Jang, S. Kimport, and H. Swisher). Springer Research Directions in Number Theory: Women in Numbers IV, accepted for publication.

• Youkow Homma, Yale University, undergraduate research student 2014.
  (Post-graduation position: Stanford University, M.S. student in Computational and Mathematical Engineering.)

• On a general class of nonsquashing partitions, (by A. Folsom, Y. Homma, J H Ryu, and B. Tong). Discrete Mathematics 339 iss. 5 (2016), 1482-1506.

• Jun Hwan (Josh) Ryu, Yale University, undergraduate research student 2014.
  (Post-graduation position: Stanford University, Ph.D. student in Psychology.)

• On a general class of nonsquashing partitions, (by A. Folsom, Y. Homma, J H Ryu, and B. Tong). Discrete Mathematics 339 iss. 5 (2016), 1482-1506.

• Benjamin Tong, Yale University, undergraduate research student 2014.
  (Post-graduation position: Hudson River Trading, NYC.)

• On a general class of nonsquashing partitions, (by A. Folsom, Y. Homma, J H Ryu, and B. Tong). Discrete Mathematics 339 iss. 5 (2016), 1482-1506.

Amherst College (2014 - present; roughly in chronological order)

• Edward (Eddie) J. Kim,Amherst College, undergraduate thesis student 2014-15.
  (Post-graduation position: Harvard University, Ph.D. student in the Graduate School of Education.)

• Undergraduate Thesis: “An application of the Circle Method in Analytic Number Theory to the Partition Function,” Amherst College, 2015.

• Caleb Ki, Amherst College, undergraduate research student 2015.
  (Post-graduation position: University of Michigan, Ph.D. student in Statistics.)

• Strange combinatorial quantum modular forms, (by A. Folsom, C. Ki, Y.N. Truong Vu, and B. Yang) Journal of Number Theory 170 (2017), 315-346.

• Yen Nhi (Nhi) Truong Vu, Amherst College, undergraduate research & thesis student 2015-16.
  (Post-graduation position: Stanford University, Ph.D. student in Mathematics.)

• Strange combinatorial quantum modular forms, (by A. Folsom, C. Ki, Y.N. Truong Vu, and B. Yang) Journal of Number Theory 170 (2017), 315-346.

• Undergraduate Thesis: “On the modular transformations and asymptotic behaviors of mock modular forms,” Amherst College, 2016.

• Bowen Yang, Amherst College, undergraduate research student 2015.
  (Post-graduation position: Caltech, Ph.D. student in Mathematics.)

• Strange combinatorial quantum modular forms, (by A. Folsom, C. Ki, Y.N. Truong Vu, and B. Yang) Journal of Number Theory 170 (2017), 315-346.

• Michael Barnett, Amherst College, undergraduate research student 2017-18.
  (Post-graduation position: ThoughtWorks)

• Quantum Jacobi forms and balanced unimodal sequences, (by M. Barnett, A. Folsom, O. Ukogu, W.J. Wesley, and H. Xu) Journal of Number Theory 186 (2018), 16-34.

• Rank generating functions for odd-balanced unimodal sequences, quantum Jacobi forms and mock Jacobi forms (by M. Barnett, A. Folsom, and W.J. Wesley), Journal of the Australian Mathematical Society 109 (2020), 157-175.

• Obinna Ukogu, Amherst College, undergraduate research student 2017.
  (Current position: University of Washington, graduate student in Mathematics)

• Quantum Jacobi forms and balanced unimodal sequences, (by M. Barnett, A. Folsom, O. Ukogu, W.J. Wesley, and H. Xu) Journal of Number Theory 186 (2018), 16-34.

• William (Jack) Wesley, Amherst College, undergraduate research & thesis student 2017-18.
  (Post-graduation position: University of California, Davis, Ph.D. student in Mathematics.)

• Quantum Jacobi forms and balanced unimodal sequences, (by M. Barnett, A. Folsom, O. Ukogu, W.J. Wesley, and H. Xu) Journal of Number Theory 186 (2018), 16-34.

• Rank generating functions for odd-balanced unimodal sequences, quantum Jacobi forms and mock Jacobi forms (by M. Barnett, A. Folsom, and W.J. Wesley), Journal of the Australian Mathematical Society 109 (2020), 157-175.

• Undergraduate Thesis: “Combinatorial Proofs of Ramanujan’s Congruences,” Amherst College, 2018.

• Hui Xu, Amherst College, undergraduate research student 2017.
  (Post-graduation position: Stanford University, Ph.D. student in Statistics.)

• Quantum Jacobi forms and balanced unimodal sequences, (by M. Barnett, A. Folsom, O. Ukogu, W.J. Wesley, and H. Xu) Journal of Number Theory 186 (2018), 16-34.

• Gregory Carroll, Amherst College, undergraduate research student 2018.
  

• Universal mock theta functions as quantum Jacobi forms, (by G. Carroll, J. Corbett, A. Folsom, and E. Thieu) Research in the Mathematical Sciences 6:6 (2019), 15pp.

• James Corbett, Amherst College, undergraduate research student 2018.
  (Post-graduation position: Lawrence Livermore National Laboratory)

• Universal mock theta functions as quantum Jacobi forms, (by G. Carroll, J. Corbett, A. Folsom, and E. Thieu) Research in the Mathematical Sciences 6:6 (2019), 15pp.

• Uyen (Ellie) Thieu, Amherst College, undergraduate research student 2018.
  (Post-graduation position: University of British Columbia, graduate student in Mathematics)

• Universal mock theta functions as quantum Jacobi forms, (by G. Carroll, J. Corbett, A. Folsom, and E. Thieu) Research in the Mathematical Sciences 6:6 (2019), 15pp.

• Justin Warring, Amherst College, undergraduate thesis student 2019 & 2020.

  • Undergraduate Thesis: "On 'Strange' Identities and Quantum Modular Forms: q-hypergeometric Identities and Modular Properties of a Peculiar Function of Kontsevich," Amherst College, 2020.

• Elizabeth Pratt, Amherst College, undergraduate research student 2020.
  (Post-graduation position: UC Berkeley, Ph.D. student in Mathematics)

  • A. Folsom, E. Pratt, N. Solomon, A.R. Tawfeek, Quantum Jacobi forms and sums of tails identities, Research in Number Theory, 8:8 (2022). 24pp.

• Noah Solomon, Amherst College, undergraduate research student 2020.
  (Post-graduation position: Georgia Tech, Ph.D. student in Mathematics)

  • A. Folsom, E. Pratt, N. Solomon, A.R. Tawfeek, Quantum Jacobi forms and sums of tails identities, Research in Number Theory, 8:8 (2022). 24pp.

• Andrew R. Tawfeek, Amherst College, undergraduate research student 2020.
  (Post-graduation position: University of Washington, Ph.D. student in Mathematics)

  • A. Folsom, E. Pratt, N. Solomon, A.R. Tawfeek, Quantum Jacobi forms and sums of tails identities, Research in Number Theory, 8:8 (2022). 24pp.

• Anna Dietrich, Amherst College, undergraduate research student 2021.
  (Post-graduation position: Brown University, Ph.D. student in Mathematics)

  • A. Dietrich, A. Folsom, K. Ng, C. Stewart, S. Xu, Overpartitions and quantum modular forms, Research in Number Theory 8:45 (2022). 16pp.

• Keane Ng, Amherst College, undergraduate research student 2021.
  (Post-graduation position: Jane Street Capital)

  • A. Dietrich, A. Folsom, K. Ng, C. Stewart, S. Xu, Overpartitions and quantum modular forms, Research in Number Theory 8:45 (2022). 16pp.

• Chloe Stewart, Amherst College, undergraduate research student 2021.
  (Post-graduation position: Colorado State University, Ph.D. student in Mathematics)

  • A. Dietrich, A. Folsom, K. Ng, C. Stewart, S. Xu, Overpartitions and quantum modular forms, Research in Number Theory 8:45 (2022). 16pp.

• Shixiong (Leo) Xu, Amherst College, undergraduate research student 2021.
  (Post-graduation position: Caltech, Ph.D. student in Mathematics)

  • A. Dietrich, A. Folsom, K. Ng, C. Stewart, S. Xu, Overpartitions and quantum modular forms, Research in Number Theory 8:45 (2022). 16pp.

• Thomas Meyer, Amherst College, undergraduate thesis student 2022-23.
  (Post-graduation position: University of Minnesota, Ph.D. student in Mathematics)

  • Undergraduate Thesis: "Resolution of the Alder-Andrews Conjecture," Amherst College, 2023.

• David Metacarpa, Amherst College, undergraduate research student 2023.
  (Post-graduation position: Office of NY State Comptroller, Program Examiner)

  • A. Folsom and D. Metacarpa, Quantum q-series and mock theta functions, Research in the Mathematical Sciences 11 no. 41 (2024), 21pp.

• Wenche Tseng, Amherst College, undergraduate research student 2023.

• Kathy Xing, Amherst College, undergraduate thesis student 2023-24.
  (Post-graduation position: University of California, Los Angeles, Ph.D. student in Mathematics)

  • Undergraduate Thesis: "Traces of Singular Moduli as the Coefficients of a Meromorphic Modular Form," Amherst College, 2024.

• John Joire, Amherst College, undergraduate research student 2024.

  • research in-progress, TBA

• Torin Steciuk, Amherst College, undergraduate research student 2024.

  • research in-progress, TBA

• Alexandre van Lidth, Amherst College, undergraduate research student 2024.

  • research in-progress, TBA